What is Chinese Remainder Theorem Calculator and Why it Matters?
CRT solves simultaneous systems of congruences and is fundamental in cryptography and modular arithmetic.
Mathematical Formula and Theory
x = Σ aᵢ Mᵢ yᵢ (mod M), where M=∏mᵢ, Mᵢ=M/mᵢ, yᵢ≡Mᵢ^{−1} (mod mᵢ).
How to Use This Calculator - Step by Step
- Enter congruences “a mod m”, one per line.
- Click Solve CRT.
Solved Example with Full Calculation
x≡2 (mod 3), x≡3 (mod 5), x≡2 (mod 7) ⇒ x≡23 (mod 105).