Consecutive Integers are Coprime/Proof 1

Theorem

$\forall h \in \Z$, $h$ and $h + 1$ have only two common factors: $1$ and $-1$.

That is, consecutive integers are always coprime.

Proof

$\gcd \set {h + 1, h} = \gcd \set {h, 1} = \gcd \set {1, 0} = 1$ from the Euclidean Algorithm.

$\blacksquare$