'number-theory' 검색 결과

Provide number theory algorithm implementations and guidance

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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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Analyze prime numbers using primality tests, factorization algorithms, prime distribution analysis, and sieve methods. Covers trial division, Miller-Rabin, Sieve of Eratosthenes, and the Prime Number Theorem. Use when determining whether an integer is prime or composite, finding prime factorizations, counting or listing primes up to a bound, or investigating prime properties within a number-theoretic proof or computation.

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

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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'.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.