Question

Hello all

What is Chinese remainder theorem ???

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Answer 1

chinese remainder theorem is a theorem of number theory, which states that if one knows the remainder of the Euclid devision of an integer n by several integers, then one can determine uniquely the remainder of the devision of n by the product of these integer under the condition that the devisiors are pairwise coprime.

Answer 2

The Chinese remainder theorem is a theorem of number theory, which states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.

The theorem was first discovered in the 3rd century AD by the Chinese mathematician Sunzi in Sunzi Suanjing.

The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers.

The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain. It has been generalized to any commutative ring, with a formulation involving ideals.

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