Chinese Remainder Theorem

Given m1,…, mr, where gcd(mi , mj) = 1, i not = j

Then the system of congruences

x = a1 mod m1

x = a2 mod m2

…..

x = ar mod mr

has a unique solution modulo M= m1 x … x mr

x = S 1<= i <= r ai Mi yi mod M

where Mi = M/mi and yi = Mi -1 mod mi

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