## What is the Chinese Remainder Theorem?

## How do you find the system of congruence using the Chinese remainder?

- The following is a general construction to find a solution to a system of congruences using the Chinese remainder theorem: . y i = N n i = n 1 n 2 ⋯ n i − 1 n i + 1 ⋯ n k. . are pairwise coprime). . v v to the system of congruences. Then u ≡ v ( m o d n 1 n 2 ⋯ n k). ). .

## Is there a proof of Sunsun-Tzu's Chinese Remainder Theorem?

- Sun-tzu's work contains neither a proof nor a full algorithm. What amounts to an algorithm for solving this problem was described by Aryabhata (6th century). Special cases of the
**Chinese remainder theorem**were also known to Brahmagupta (7th century), and appear in Fibonacci 's Liber Abaci (1202).

## What is the remainder when divided by 60?

- In the above example, the product is 3*4*5 = 60. And 11 is one solution, other solutions are 71, 131, .. etc. All these solutions produce the same
**remainder**when divided by 60, i.e., they are of form 11 + m*60 where m >= 0.

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