Let $a,b \in \mathbb{Z}^+ $. If $b\mid a$ and $b\mid (a+2)$ , prove that $b=1$ or $b=2$

I like the start up to $ b \mid 2$.

The following steps can be simplified. Either:

  • An integer $m$ that divides another one $n$ is smaller or equal to $n$. Therefore $b \in \{1,2\}$.
  • Or the only natural integers that divide $2$ are $1$ and $2$.

Tags:

Integers

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