Cancellability of Congruences/Corollary 1/Proof 1

Corollary to Cancellability of Congruences

Let $c$ and $n$ be coprime integers, that is:

$c \perp n$

Then:

$c a \equiv c b \pmod n \implies a \equiv b \pmod n$

Proof

Recall that $c \perp n$ means $\gcd \set {c, n} = 1$.

The result follows directly from Cancellability of Congruences.

$\blacksquare$