Congruence Solver (CRT)

The coefficient of x in ax ≡ b (mod m). The congruence is solvable exactly when gcd(a, m) divides b.

The right-hand side of ax ≡ b (mod m) — the remainder that ax must leave when divided by m.

The modulus of the congruence. All solution classes modulo m are listed — there are gcd(a, m) of them when solutions exist.

One congruence per line as remainder, modulus: the line 2, 3 means x ≡ 2 (mod 3).

The Chinese Remainder Theorem combines them into a single answer modulo the product of the moduli.