Prove directly from the definition of congruence modulo n that if a,c, and n are integers,
Let a, c and n be integers such that n>1.
We have to prove that if
So, by the definition of congruence modulo n,
If n divides
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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