Consecutive Integers are Coprime/Proof 3

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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

A direct application of GCD of Integer with Integer + $n$:

$\gcd \set {a, a + n} \divides n$

$\blacksquare$


Sources