Modular arithmetic workspace

Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Search and sort the first 200 preview rows. Copy result copies the summary. Download JSON or CSV for every result and worked step. Geometry tools also provide a downloadable SVG diagram. Choose linear congruence a*x ≡ b mod modulus, modular inverse, or a system of up to 32 residue/modulus pairs. Moduli must be integers at least two. The extended Euclidean algorithm supplies Bezout coefficients and division steps. A linear congruence exists exactly when gcd(a,modulus) divides b. Compatible non-coprime systems are combined using generalized CRT; incompatible systems report no solution. A residue and positive period parameterize every integer solution without enumerating a huge residue set. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Up to 100,000 characters. Review the settings before running.