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Chinese remainder theorem For any a b and coprime m n there exists a unique x (mod mn) such that x ≡ a (mod m) and x ≡ b (mod n) In fact x ≡ b m n –1 m + a n m –1 n (mod mn) where m n −1 is the inverse of m modulo n and n m −1 is the inverse of n modulo m.
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Wikipedia Modular arithmetic
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a≡b (mod m) is read as “a is congruent to b mod m” In a simple but not wholly correct way we can think of a≡b (mod m) to mean “a is the remainder when b is divided by m” For instance 2≡12 (mod 10) means that 2 is the remainder when 12 is divided by 10.