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$ x = 5 (mod 7) $Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
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If $x \equiv a ~ (n)$ and $x\equiv b ~ (m)$ where $n,m$ are relatively prime positive integers then $x\equiv ab ~ (nm)$.Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
How to proceed?
This problem is of historical importance because it illustrates the method used by the chinese generals in the Middle Age to know the number of soldiers in a battalion. The general solution of this problem is illustrated in...Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13).
How to proceed?