Question

Describe the history of the chinese remainder theorem. Describe some of the relevant problems posed in chinese and hindu writings and how the chinese remainder theorem applies to them

Answer 1

Answer:

In number theory, the Chinese remainder theorem 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 earliest known statement of the theorem is by the Chinese mathematician Sunzi in Sunzi Suanjing in the 3rd century AD.

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.

Explanation:

Answer 2

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