Question:
What is the Chinese remainder theorem as it applies to solving equations
involving the modulus operator?

Replies:
Any introductory text on number theory should have this. I quote from
Elementary Introduction to Number Theory by C. T. Long, D. C. Heath & Co.,
1965.

"The Chinese Remainder Theorem: if (Mi,Mj) = 1 for i != j, then the system
x == C1 (mod M1), x == C2 (mod M2), . . . , x == Cr (mod Mr) is solvable
and the solution is unique modulo M where M = M1 * M2 * ... * Mr. . . .
Such problems were studied in antiquity, particularly by ancient Chinese
mathematicians, so the solution to the problem is called the Chinese
remainder theorem.

(above: I have used == for "is congruent to" and ! = for "not equal to")

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