Chinese remainder theorem (Çin Kalan Teoremi) (CRT)

Theorem 2.1.11 (Chinese remainder theorem, CRT) : If the integers n1,n2,... ,nk are pairwise relatively prime, then the system of simultaneous congruences

x ≡ a1 (mod n1)

x ≡ a2 (mod n2)

.

.

.

x ≡ ak (mod nk)

has a unique solution modulo n = n1n2 ···nk.

Example 2.1.7 The pair of congruences x ≡ 3(mod 7), x ≡ 7(mod 13) has a unique solution

x ≡ 59 (mod 91).