本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261106-r06-linear-diophantine-equation-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":12,"b":18,"c":12}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(12, 18, 12, 6, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(12, 18, 12, 6, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-18,"b":27,"c":19}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-18, 27, 19, 9, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-18, 27, 19, 9, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":24,"b":36,"c":24}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(24, 36, 24, 12, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(24, 36, 24, 12, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-30,"b":45,"c":31}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-30, 45, 31, 15, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-30, 45, 31, 15, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":36,"b":54,"c":36}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(36, 54, 36, 18, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(36, 54, 36, 18, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-42,"b":63,"c":43}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-42, 63, 43, 21, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-42, 63, 43, 21, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":48,"b":72,"c":48}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(48, 72, 48, 24, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(48, 72, 48, 24, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-54,"b":81,"c":55}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-54, 81, 55, 27, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-54, 81, 55, 27, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":60,"b":90,"c":60}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(60, 90, 60, 30, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(60, 90, 60, 30, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-66,"b":99,"c":67}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-66, 99, 67, 33, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-66, 99, 67, 33, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":72,"b":108,"c":72}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(72, 108, 72, 36, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(72, 108, 72, 36, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-78,"b":117,"c":79}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-78, 117, 79, 39, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-78, 117, 79, 39, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":84,"b":126,"c":84}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(84, 126, 84, 42, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(84, 126, 84, 42, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-90,"b":135,"c":91}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-90, 135, 91, 45, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-90, 135, 91, 45, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":96,"b":144,"c":96}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(96, 144, 96, 48, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(96, 144, 96, 48, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-102,"b":153,"c":103}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-102, 153, 103, 51, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-102, 153, 103, 51, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":108,"b":162,"c":108}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(108, 162, 108, 54, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(108, 162, 108, 54, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-114,"b":171,"c":115}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-114, 171, 115, 57, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-114, 171, 115, 57, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":120,"b":180,"c":120}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(120, 180, 120, 60, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(120, 180, 120, 60, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-126,"b":189,"c":127}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-126, 189, 127, 63, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-126, 189, 127, 63, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":132,"b":198,"c":132}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(132, 198, 132, 66, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(132, 198, 132, 66, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-138,"b":207,"c":139}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-138, 207, 139, 69, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-138, 207, 139, 69, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":144,"b":216,"c":144}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(144, 216, 144, 72, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(144, 216, 144, 72, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":-150,"b":225,"c":151}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(-150, 225, 151, 75, 否, 否, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(-150, 225, 151, 75, 否, 否, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-solvability；資料={"a":156,"b":234,"c":156}。請依 [a, b, c, gcd, both_coefficients_zero, solvable, boundary] 欄序回答。
(156, 234, 156, 78, 否, 是, gcd_divides_c_iff_integer_solution)
Wave5封閉層核對=(156, 234, 156, 78, 否, 是, gcd_divides_c_iff_integer_solution)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-solvability · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":12,"b":18,"c":6}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(6, -1, 1, -1, 1, 6, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(6, -1, 1, -1, 1, 6, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-18,"b":27,"c":18}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(9, 1, 1, 2, 2, 18, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(9, 1, 1, 2, 2, 18, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":24,"b":36,"c":36}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(12, -1, 1, -3, 3, 36, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(12, -1, 1, -3, 3, 36, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-30,"b":45,"c":60}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(15, 1, 1, 4, 4, 60, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(15, 1, 1, 4, 4, 60, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":36,"b":54,"c":90}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(18, -1, 1, -5, 5, 90, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(18, -1, 1, -5, 5, 90, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-42,"b":63,"c":126}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(21, 1, 1, 6, 6, 126, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(21, 1, 1, 6, 6, 126, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":48,"b":72,"c":168}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(24, -1, 1, -7, 7, 168, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(24, -1, 1, -7, 7, 168, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-54,"b":81,"c":216}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(27, 1, 1, 8, 8, 216, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(27, 1, 1, 8, 8, 216, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":60,"b":90,"c":270}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(30, -1, 1, -9, 9, 270, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(30, -1, 1, -9, 9, 270, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-66,"b":99,"c":330}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(33, 1, 1, 10, 10, 330, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(33, 1, 1, 10, 10, 330, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":72,"b":108,"c":396}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(36, -1, 1, -11, 11, 396, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(36, -1, 1, -11, 11, 396, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-78,"b":117,"c":468}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(39, 1, 1, 12, 12, 468, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(39, 1, 1, 12, 12, 468, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":84,"b":126,"c":546}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(42, -1, 1, -13, 13, 546, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(42, -1, 1, -13, 13, 546, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-90,"b":135,"c":630}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(45, 1, 1, 14, 14, 630, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(45, 1, 1, 14, 14, 630, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":96,"b":144,"c":720}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(48, -1, 1, -15, 15, 720, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(48, -1, 1, -15, 15, 720, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-102,"b":153,"c":816}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(51, 1, 1, 16, 16, 816, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(51, 1, 1, 16, 16, 816, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":108,"b":162,"c":918}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(54, -1, 1, -17, 17, 918, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(54, -1, 1, -17, 17, 918, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-114,"b":171,"c":1026}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(57, 1, 1, 18, 18, 1026, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(57, 1, 1, 18, 18, 1026, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":120,"b":180,"c":1140}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(60, -1, 1, -19, 19, 1140, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(60, -1, 1, -19, 19, 1140, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-126,"b":189,"c":1260}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(63, 1, 1, 20, 20, 1260, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(63, 1, 1, 20, 20, 1260, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":132,"b":198,"c":1386}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(66, -1, 1, -21, 21, 1386, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(66, -1, 1, -21, 21, 1386, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-138,"b":207,"c":1518}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(69, 1, 1, 22, 22, 1518, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(69, 1, 1, 22, 22, 1518, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":144,"b":216,"c":1656}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(72, -1, 1, -23, 23, 1656, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(72, -1, 1, -23, 23, 1656, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":-150,"b":225,"c":1800}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(75, 1, 1, 24, 24, 1800, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(75, 1, 1, 24, 24, 1800, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-particular-solution；資料={"a":156,"b":234,"c":1950}。請依 [gcd, bezout_x, bezout_y, x0, y0, linear_combination, certificate_valid, certificate] 欄序回答。
(78, -1, 1, -25, 25, 1950, 是, extended_Euclidean_Bezout_certificate)
Wave5封閉層核對=(78, -1, 1, -25, 25, 1950, 是, extended_Euclidean_Bezout_certificate)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-particular-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":12,"b":18,"c":6}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-1, 1, 3, -2, x=-1+(3)t, y=1+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-1, 1, 3, -2, x=-1+(3)t, y=1+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-18,"b":27,"c":18}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(2, 2, 3, 2, x=2+(3)t, y=2+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(2, 2, 3, 2, x=2+(3)t, y=2+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":24,"b":36,"c":36}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-3, 3, 3, -2, x=-3+(3)t, y=3+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-3, 3, 3, -2, x=-3+(3)t, y=3+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-30,"b":45,"c":60}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(4, 4, 3, 2, x=4+(3)t, y=4+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(4, 4, 3, 2, x=4+(3)t, y=4+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":36,"b":54,"c":90}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-5, 5, 3, -2, x=-5+(3)t, y=5+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-5, 5, 3, -2, x=-5+(3)t, y=5+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-42,"b":63,"c":126}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(6, 6, 3, 2, x=6+(3)t, y=6+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(6, 6, 3, 2, x=6+(3)t, y=6+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":48,"b":72,"c":168}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-7, 7, 3, -2, x=-7+(3)t, y=7+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-7, 7, 3, -2, x=-7+(3)t, y=7+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-54,"b":81,"c":216}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(8, 8, 3, 2, x=8+(3)t, y=8+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(8, 8, 3, 2, x=8+(3)t, y=8+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":60,"b":90,"c":270}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-9, 9, 3, -2, x=-9+(3)t, y=9+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-9, 9, 3, -2, x=-9+(3)t, y=9+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-66,"b":99,"c":330}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(10, 10, 3, 2, x=10+(3)t, y=10+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(10, 10, 3, 2, x=10+(3)t, y=10+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":72,"b":108,"c":396}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-11, 11, 3, -2, x=-11+(3)t, y=11+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-11, 11, 3, -2, x=-11+(3)t, y=11+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-78,"b":117,"c":468}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(12, 12, 3, 2, x=12+(3)t, y=12+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(12, 12, 3, 2, x=12+(3)t, y=12+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":84,"b":126,"c":546}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-13, 13, 3, -2, x=-13+(3)t, y=13+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-13, 13, 3, -2, x=-13+(3)t, y=13+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-90,"b":135,"c":630}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(14, 14, 3, 2, x=14+(3)t, y=14+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(14, 14, 3, 2, x=14+(3)t, y=14+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":96,"b":144,"c":720}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-15, 15, 3, -2, x=-15+(3)t, y=15+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-15, 15, 3, -2, x=-15+(3)t, y=15+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-102,"b":153,"c":816}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(16, 16, 3, 2, x=16+(3)t, y=16+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(16, 16, 3, 2, x=16+(3)t, y=16+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":108,"b":162,"c":918}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-17, 17, 3, -2, x=-17+(3)t, y=17+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-17, 17, 3, -2, x=-17+(3)t, y=17+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-114,"b":171,"c":1026}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(18, 18, 3, 2, x=18+(3)t, y=18+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(18, 18, 3, 2, x=18+(3)t, y=18+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":120,"b":180,"c":1140}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-19, 19, 3, -2, x=-19+(3)t, y=19+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-19, 19, 3, -2, x=-19+(3)t, y=19+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-126,"b":189,"c":1260}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(20, 20, 3, 2, x=20+(3)t, y=20+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(20, 20, 3, 2, x=20+(3)t, y=20+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":132,"b":198,"c":1386}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-21, 21, 3, -2, x=-21+(3)t, y=21+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-21, 21, 3, -2, x=-21+(3)t, y=21+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-138,"b":207,"c":1518}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(22, 22, 3, 2, x=22+(3)t, y=22+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(22, 22, 3, 2, x=22+(3)t, y=22+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":144,"b":216,"c":1656}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-23, 23, 3, -2, x=-23+(3)t, y=23+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-23, 23, 3, -2, x=-23+(3)t, y=23+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":-150,"b":225,"c":1800}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(24, 24, 3, 2, x=24+(3)t, y=24+(2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(24, 24, 3, 2, x=24+(3)t, y=24+(2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-general-solution；資料={"a":156,"b":234,"c":1950}。請依 [x0, y0, step_x, step_y, x_formula, y_formula, certificate] 欄序回答。
(-25, 25, 3, -2, x=-25+(3)t, y=25+(-2)t, all_and_only_integer_solutions_for_t_in_Z)
Wave5封閉層核對=(-25, 25, 3, -2, x=-25+(3)t, y=25+(-2)t, all_and_only_integer_solutions_for_t_in_Z)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-general-solution · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-12}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-12, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-12, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-11}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-11, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-11, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-10}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-10, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-10, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-9}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-9, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-9, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-8}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-8, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-8, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-7}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-7, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-7, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-6}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-6, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-6, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-5}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-5, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-5, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-4}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-4, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-4, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-3}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-3, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-3, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-2}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-2, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-2, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":-1}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(-1, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(-1, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":0}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(0, 是, all_integer_pairs, never_divide_by_gcd_zero)
Wave5封閉層核對=(0, 是, all_integer_pairs, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":1}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(1, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(1, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":2}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(2, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(2, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":3}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(3, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(3, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":4}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(4, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(4, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":5}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(5, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(5, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":6}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(6, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(6, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":7}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(7, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(7, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":8}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(8, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(8, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":9}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(9, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(9, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":10}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(10, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(10, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":11}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(11, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(11, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate
exact integer coefficients、normalized gcd與extended Euclidean證書。操作=dioph-degenerate-boundary；資料={"a":0,"b":0,"c":12}。請依 [c, solvable, solution_set, boundary] 欄序回答。
(12, 否, no_integer_solution, never_divide_by_gcd_zero)
Wave5封閉層核對=(12, 否, no_integer_solution, never_divide_by_gcd_zero)；依完整明示資料獨立重算；非退化ax+by=c有解iff gcd(a,b)整除c，完整解需Z參數化而非有限搜尋；a=b=0須分開處理且不得除以gcd零；保留零係數與負係數。
線性Diophantine方程 · qf-mod37-dioph-degenerate-boundary · candidate