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Chinese Remainder Theorem Solver

Find the unique integer that satisfies multiple simultaneous modular congruences. Use this when solving scheduling puzzles, cryptographic problems, or any system where a number must leave specific remainders under different divisors.

First Remainder (r₁)

First Modulus (m₁)

Second Remainder (r₂)

Second Modulus (m₂)

Third Remainder (r₃) - Optional

Third Modulus (m₃) - Optional

Fill in the required fields to see your result.

Number Theory

Chinese Remainder Theorem Calculator

Finds the smallest non-negative integer x satisfying a system of two or three simultaneous modular congruences. Used in cryptography, scheduling problems, and number theory proofs.

First Remainder (a₁)

First Modulus (m₁)

Second Remainder (a₂)

Second Modulus (m₂)

Third Remainder (a₃, Optional)

Third Modulus (m₃, Optional)

Fill in the required fields to see your result.

Key differences

	Chinese Remainder Theorem Solver	Chinese Remainder Theorem Calculator
Category	Number Theory	Number Theory
Inputs required	6	6
Result	Solution (x)	Solution (x)
What it does	Find the unique integer that satisfies multiple simultaneous modular congruences. Use this when solving scheduling puzzles, cryptographic problems, or any system where a number must leave specific remainders under different divisors.	Finds the smallest non-negative integer x satisfying a system of two or three simultaneous modular congruences. Used in cryptography, scheduling problems, and number theory proofs.