let n belongs to N and let a, b belong to Z. prove that a is...

let n belongs to N and let a, b belong to Z. prove that a is congruent to b, mod n, if and only if a and b have the same remainder when divided by n.

Expert Solution

Here I'm using division algorithm theorem that is if and b any two integer atleast one is nonzero then by division theorem b=aq+r where r is less than a. also q and r are quotient and remainder. solution is below both if and only if .Thank you.

Colby Messinger answered 2 years ago

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