basic

Chinese Remainder Theorem Two Congruences Calculator

x ≡ a₁ (mod m₁), x ≡ a₂ (mod m₂) — CRT solution.

Solves a system of two linear congruences using the Chinese Remainder Theorem. Requires the user to provide the modular inverse of m₁ mod m₂ (for coprime moduli).

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

x = a₁ + m₁ × ((a₂−a₁) × inv(m₁,m₂) mod m₂); period = m₁×m₂

In depth

Solves a system of two linear congruences using the Chinese Remainder Theorem. Requires the user to provide the modular inverse of m₁ mod m₂ (for coprime moduli).