// multi-utility computation suite · offline · instant · precise
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math.chinese-remainder Calculator
Solves systems of simultaneous congruences using the Chinese Remainder Theorem and finds the unique solution modulo the LCM. CRT is fundamental to cryptography (RSA with CRT optimisation), computer arithmetic, and modular number theory.
Inputs
N1
Reference formula or conversion factor shown for context.
R1
Reference formula or conversion factor shown for context.
N2
Reference formula or conversion factor shown for context.
R2
Reference formula or conversion factor shown for context.
Results
x (smallest positive solution)
Sample size or count used in the calculation.
x ≡
Reference formula or conversion factor shown for context.
modulus N = n1×n2
Sample size or count used in the calculation.
general solution
Sample size or count used in the calculation.
CRT theorem
Reference formula or conversion factor shown for context.