# OCME · Knowledge & practice explorer

302 MKO / 1,441 families / 360 batches / 36,000 questions.

36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training.

100 results; page 3/4.

## Question 23351: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0051`; number: 23351
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0051/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0051/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0051.json)

## Question 23352: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0052`; number: 23352
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0052/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0052/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0052.json)

## Question 23353: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0053`; number: 23353
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0053/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0053/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0053.json)

## Question 23354: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0054`; number: 23354
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0054/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0054/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0054.json)

## Question 23355: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0055`; number: 23355
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0055/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0055/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0055.json)

## Question 23356: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0056`; number: 23356
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0056/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0056/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0056.json)

## Question 23357: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0057`; number: 23357
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0057/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0057/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0057.json)

## Question 23358: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0058`; number: 23358
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0058/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0058/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0058.json)

## Question 23359: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0059`; number: 23359
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0059/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0059/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0059.json)

## Question 23360: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0060`; number: 23360
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0060/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0060/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0060.json)

## Question 23361: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0061`; number: 23361
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0061/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0061/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0061.json)

## Question 23362: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0062`; number: 23362
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0062/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0062/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0062.json)

## Question 23363: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0063`; number: 23363
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0063/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0063/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0063.json)

## Question 23364: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0064`; number: 23364
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0064/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0064/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0064.json)

## Question 23365: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0065`; number: 23365
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0065/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0065/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0065.json)

## Question 23366: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0066`; number: 23366
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0066/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0066/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0066.json)

## Question 23367: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0067`; number: 23367
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0067/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0067/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0067.json)

## Question 23368: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0068`; number: 23368
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0068/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0068/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0068.json)

## Question 23369: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0069`; number: 23369
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0069/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0069/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0069.json)

## Question 23370: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0070`; number: 23370
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0070/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0070/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0070.json)

## Question 23371: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0071`; number: 23371
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0071/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0071/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0071.json)

## Question 23372: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0072`; number: 23372
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0072/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0072/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0072.json)

## Question 23373: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0073`; number: 23373
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0073/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0073/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0073.json)

## Question 23374: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0074`; number: 23374
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0074/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0074/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0074.json)

## Question 23375: A Nonzero Residue Modulo an Odd Prime Has Two Distinct Opposite Roots

- ID: `q-20261014-advance-20261111-r06-quadratic-residue-0075`; number: 23375
- Processing: second_context_reviewed
- MKO: [mko-quadratic-residue](/en/mko/mko-quadratic-residue/)
- Family: [qf-mod42-quadratic-paired-roots](/en/explore/?family=qf-mod42-quadratic-paired-roots)
- Batch: [batch-20261014-advance-20261111-r06-quadratic-residue-foundations](/en/explore/?batch=batch-20261014-advance-20261111-r06-quadratic-residue-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0075/) / [Markdown](/en/questions/q-20261014-advance-20261111-r06-quadratic-residue-0075/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261111-r06-quadratic-residue-0075.json)

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