Cancellability of Congruences/Corollary 2
Corollary to Cancellability of Congruences
Let $a, b, c$ be integers.
Let $p$ be a prime number such that $p \nmid c$.
- $c a \equiv c b \pmod p \implies a \equiv b \pmod p$
where $\equiv$ denotes congruence.
As $p \nmid c$, it follows from Prime not Divisor implies Coprime that:
- $p \perp c$
where $\perp$ denotes that $p$ and $c$ are coprime.
The result follows from Cancellability of Congruences: Corollary 1.