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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.

Number Theory

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.

Key differences

	Chinese Remainder Theorem Calculator	Chinese Remainder Theorem Solver
Category	Number Theory	Number Theory
Inputs required	6	6
Result	Solution (x)	Solution (x)
What it does	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.	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.