'diophantine' 검색 결과

Solve Diophantine equations (integer-only solutions) including linear, quadratic, and Pell equations. Covers the extended Euclidean algorithm, descent methods, and existence proofs. Use when finding all integer solutions to ax + by = c, solving Pell's equation, generating Pythagorean triples, proving no integer solutions exist via modular constraints, or finding the fundamental solution from which all others are generated.

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Expert-level number theory knowledge. Use when working with divisibility, prime numbers, modular arithmetic, congruences, Diophantine equations, cryptography, quadratic residues, or analytic number theory. Also use when the user mentions 'prime', 'divisibility', 'modular arithmetic', 'congruence', 'GCD', 'Euler totient', 'Fermat little theorem', 'Chinese remainder theorem', 'quadratic residue', 'Diophantine equation', 'RSA', or 'prime factorization'.

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Number theory expert covering primes, divisibility, modular arithmetic, Diophantine equations, and cryptographic applications

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.