OlmekinjP

2021-01-04

Prove directly from the definition of congruence modulo n that if a,c, and n are integers,

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Skilled2021-01-05Added 92 answers

Step 1

Let a, c and n be integers such that n>1.

We have to prove that if

Note that,

So, by the definition of congruence modulo n,

If n divides

Step 2

Since a and c are integers,

Now, n divides any integer multiple of (a−c) implies that n divides

But, by the algebraic identity

So, we can say that n divides

Therefore, by the definition of congruence modulo n,

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