{"schema_version":"ocme-public-explorer-results-v1","locale":"zh-Hant","filters":{"mko":"mko-euler-theorem-number-theory"},"total":100,"page":1,"page_count":4,"question_state":"candidate","english_state":"ai_candidate","canonical_truth_promotion":false,"entries":[{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0001","number":20001,"title":{"zh-Hant":"第 20001 題：Euler定理","en":"Question 20001: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"051b1b881628aa0e6762cd9774857a72cd596f59ca175ab8ba286ff9973191c2","derivation_sha256":"372f244c6ac319d2ec6e5f8ab805f139eb66eae756f382da6c4e3b1c1c0030c0"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0002","number":20002,"title":{"zh-Hant":"第 20002 題：Euler定理","en":"Question 20002: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"9f7cebe8797bad9375b20279db09af7e14ec4c30f3d8edf4a1753a55d08b5b73","derivation_sha256":"b316b4fc9249c99bd7b8ee4f11d7adb7868a67393519699bff4996d3aa6b59a7"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0003","number":20003,"title":{"zh-Hant":"第 20003 題：Euler定理","en":"Question 20003: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"1e8148fd88032a46ba0af8f19312ffcf42fff6138a69e50b2cbd326fa5420533","derivation_sha256":"bcd0c67f15946f0f11a86d4c6f3a08bc2a0b24a9f5eed0e4f0a61b21a057757a"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0004","number":20004,"title":{"zh-Hant":"第 20004 題：Euler定理","en":"Question 20004: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"ed6e57855dde931135ad20c630b7bef8c48e7a90ae4719d5c5e4b7b85bb99417","derivation_sha256":"e43f1f0f63512378d7a7f2fe8cfa535af1b38657c5ab9a1154653d68b21b7f61"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0005","number":20005,"title":{"zh-Hant":"第 20005 題：Euler定理","en":"Question 20005: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"692e456156eeebcc118db1da4740c8d88e8e85310b8864ddabff42de8e50e03c","derivation_sha256":"e8d8a46706ececaf68a948416f4f81635cf5dd1b7c10940917a6c2d64bd72f70"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0006","number":20006,"title":{"zh-Hant":"第 20006 題：Euler定理","en":"Question 20006: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"3da730110053d84d34a660f8a9192a09c3d77fe14a71a9e936b86bf8810ec4a8","derivation_sha256":"9b8fec9c7c5e1460f15111841ad8c2482ea95eb137ec637c68338693af1ed0a0"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0007","number":20007,"title":{"zh-Hant":"第 20007 題：Euler定理","en":"Question 20007: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"a94f1a18699eea2e3dabaae0e41859477f0b85ae4173cbe98e4edaea7a5598e3","derivation_sha256":"ee803a2bb18d0832d41e2de75b96b80fda8e2a15b05f948b7cebe50508a06834"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0008","number":20008,"title":{"zh-Hant":"第 20008 題：Euler定理","en":"Question 20008: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"4afdf1cd23c0cab820627033678d619204df5058d5ba420e49e8c7e7a0d26829","derivation_sha256":"84cded01c4e04f990b8e50082428ce332bf35542ebd771ae8c8ad3e42aeef78b"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0009","number":20009,"title":{"zh-Hant":"第 20009 題：Euler定理","en":"Question 20009: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"6705fe0affde78b7222c9fdc094a172f0fdb72e717b31b1a15524c5bbd7d44e9","derivation_sha256":"b3140111143138a6f65bcd46e648d418c58b27e0f6df386df964872a246563ae"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0010","number":20010,"title":{"zh-Hant":"第 20010 題：Euler定理","en":"Question 20010: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"0643a54dd1d06e77e7df2aeadd89d9534262ca7e4521d8e8e6634311699cdd6d","derivation_sha256":"6de1946d37420c0e2418c8f0469519fcdbf963fd059fb9de2045f3a2e2befbd7"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0011","number":20011,"title":{"zh-Hant":"第 20011 題：Euler定理","en":"Question 20011: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"0a79e4bf42689053e0da517b1df0f2c47e1788356d4334f9de9ae9e0a36eb89a","derivation_sha256":"92e38b1ae9cd20ba255d7502f6c18e11a1050294fc0e83d1e9cb80a0c4b9beb3"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0012","number":20012,"title":{"zh-Hant":"第 20012 題：Euler定理","en":"Question 20012: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"992bc6d95ad77230b9552217a8bf24fc82eeacbe609e542c1cc141cd786ca137","derivation_sha256":"b41812380e4b0dd463759c1ad0999d1cc5919655fd32baa99e45666ff70ce65b"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0013","number":20013,"title":{"zh-Hant":"第 20013 題：Euler定理","en":"Question 20013: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"5d8c94bb346cb3231c8e6ca4f48dd3cbd3cd1f1dd21fa98080bbaf4da4e8458b","derivation_sha256":"2bd6b186f77b377f9ac2aac2b0bb43573935dc2491b7c083cfcf4c9f23879924"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0014","number":20014,"title":{"zh-Hant":"第 20014 題：Euler定理","en":"Question 20014: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"622473a4c109a0a056bcee0a888acdaf505ebdcf4c9382a156fc3668f16218f8","derivation_sha256":"70c571c203c70be258b21682aa17dc3c5407bfa0271666adc79f20a228ea3190"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0015","number":20015,"title":{"zh-Hant":"第 20015 題：Euler定理","en":"Question 20015: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"679858394ab864f21f27ebb7cb0b9a4096fb08871fe39b5704c78e910e732543","derivation_sha256":"bdee30be993203c66a6312a0d042ea402fa90624891dbd38cc7fbe29167d453b"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0016","number":20016,"title":{"zh-Hant":"第 20016 題：Euler定理","en":"Question 20016: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"58e7d09e3dbcf3f474a35bb0a77ca6cd6ee837de0e63f57fda3801e9eda1244e","derivation_sha256":"5dd4280733d69aa98eea33bb047635b6c27e55e23eccbbdabeb44ffa5896434d"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0017","number":20017,"title":{"zh-Hant":"第 20017 題：Euler定理","en":"Question 20017: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"ea4bcf2b72df53f1c0196fe62bae9df407e02149a9d294c2f2d38323da99235a","derivation_sha256":"7e7c9f5fc174f24f0566b895dc5cd36bb70a716f9dde97f93e8311c5c9da8e2c"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0018","number":20018,"title":{"zh-Hant":"第 20018 題：Euler定理","en":"Question 20018: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"139823f16cb92aa301bd8ec896a3579605b53404054547f116822aeade00409f","derivation_sha256":"2132beea8b0b4636b1f99beb36fb3c06af69b57a5c03609b9e0ecf0a1abc0c91"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0019","number":20019,"title":{"zh-Hant":"第 20019 題：Euler定理","en":"Question 20019: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"4cf5214de5a797f346972ee345f75a829bd0513eba90c3556b92633e56c074f8","derivation_sha256":"907e2195f3dabbed4435b4dda97a9c14578195dc136e32df2cce1bee80ebff62"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0020","number":20020,"title":{"zh-Hant":"第 20020 題：Euler定理","en":"Question 20020: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"53e757ffc21bb71b84ce165c11584d39e5a6e4f282f811ab8f8e36d9d23e54dd","derivation_sha256":"b0d6846f4147fe39bad5a268ede9a2d1cac694da3f55e01598352099f29fb100"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0021","number":20021,"title":{"zh-Hant":"第 20021 題：Euler定理","en":"Question 20021: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"8d44b86e5c5f6ec4687b1a763816c9d4224dd77e2ede52acf8ecf79dabbac5a7","derivation_sha256":"8dcd10bc259b7701b300bdbb28816263cf74ceaa48732fc2741ec121e1c672b9"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0022","number":20022,"title":{"zh-Hant":"第 20022 題：Euler定理","en":"Question 20022: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"c42477534741f16a7e77546618c67f071825ad0c35f1cdc365b2867f1c6b97b9","derivation_sha256":"9fc7de5c152f3254acb860a8ea9bd75ff87cb5f20f9adbde10da29de4fdc7ae7"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0023","number":20023,"title":{"zh-Hant":"第 20023 題：Euler定理","en":"Question 20023: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"da78d64d7c0a2253feb5902179b7497996d55db6d216f9b9dea7c5e49775e23f","derivation_sha256":"11cafe44be4b2d7b8c7ce5630c6e4d0501bc41701648c5ba9d55f926161add89"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0024","number":20024,"title":{"zh-Hant":"第 20024 題：Euler定理","en":"Question 20024: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"742392a3a56f4762e84f9b4146f69815381a7e7767136085cc83ef6ef4c508c1","derivation_sha256":"0ef528b4c902dc9a456544000ba976c37d271609bf97893d90933bf55df56080"},{"question_id":"q-20261014-advance-20261107-r06-euler-theorem-number-theory-0025","number":20025,"title":{"zh-Hant":"第 20025 題：Euler定理","en":"Question 20025: Euler Congruence Requires a Unit Residue, Not a Prime Modulus"},"family_id":"qf-mod38-eulerthm-congruence","batch_id":"batch-20261014-advance-20261107-r06-euler-theorem-number-theory-foundations","mko_ids":["mko-euler-theorem-number-theory"],"question_state":"candidate","english_state":"ai_candidate","processing_state":"second_context_reviewed","source_question_sha256":"568586b8180bfc83c31faa4e4fdfa5a145dc25bde792d14906a6179081f1cdea","derivation_sha256":"64e901f25f46a4f37143afb5a176824714b2c83b0f614d39b454ee41def49ec4"}]}