Chinese Remainder Theorem

The Chinese remainder theorem reconstructs an integer from compatible congruences with pairwise coprime moduli.

See Worked Example Open Math Solver →

Meaning

What Is Chinese Remainder Theorem?

The Chinese remainder theorem reconstructs an integer from compatible congruences with pairwise coprime moduli.

Examples

1x≡2 mod 3 and x≡3 mod 5 has solution x≡8 mod 15.

Understand

Know the definition and standard notation for Chinese Remainder Theorem.
Be able to recognise or compute chinese remainder theorem in a small example.
Connect the concept to nearby topics in the same subject before using it in larger CSE problems.

CSE Connection

Used in cryptography, hashing, coding theory, security protocols and efficient integer algorithms.

FAQ

What is Chinese Remainder Theorem?

The Chinese remainder theorem reconstructs an integer from compatible congruences with pairwise coprime moduli.

Why is Chinese Remainder Theorem useful in computer science?

Used in cryptography, hashing, coding theory, security protocols and efficient integer algorithms.