Chinese Remainder Theorem

Author

Eric W. Weisstein
July 23, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/ChineseRemainderTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ChineseRemainderTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<NumberTheory`NumberTheoryFunctions`

Usage

?ChineseRemainder

Examples

ChineseRemainder[{1,1,1},{3,5,7}]

%+LCM[3,5,7]

Using Reduce

Requires v5.0

soln=Reduce[x==3k+1==5l+1==7m+1&&k>0&&l>0&&m>0&&Element[k|l|m|x,Integers],{k,l,m,x}]

Table[soln /. C[1]:>n,{n,5}]