“Chinese Remainder Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Chinese Remainder Theorem

释义

Chinese Remainder Theorem

Let and be Positive Integers which are Relatively Prime and let and be any twoIntegers. Then there is an Integer such that

(1)

and

(2)

Moreover,

is uniquely determined modulo

. An equivalent statement is that if

, then every pair ofResidue Classes modulo

and

corresponds to a simple Residue Class modulo

The theorem can also be generalized as follows. Given a set of simultaneous Congruences

(3)

for

, ...,

and for which the

are pairwise Relatively Prime, the solution of the set ofCongruences is

(4)

where

(5)

and the

are determined from

(6)

References

Ireland, K. and Rosen, M. ``The Chinese Remainder Theorem.'' §3.4 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 34-38, 1990.

Uspensky, J. V. and Heaslet, M. A. Elementary Number Theory. New York: McGraw-Hill, pp. 189-191, 1939.

Wagon, S. ``The Chinese Remainder Theorem.'' §8.4 in Mathematica in Action. New York: W. H. Freeman, pp. 260-263, 1991.

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