Exercise 1.2.35 ($(a,a+2) = 1$ or $2$)

Question

Prove that $(a,a+2) = 1$ or $2$ for every integer $a$.

Richard Ganaye · Accepted Answer

Put $d = a \wedge (a+2)$. Then $d \mid a$ and $d \mid a+2$, thus $d \mid (a+2) - a = 2$. From $d \mid 2$, where $d \geq 0$, we deduce $d = 1$ or $d = 2$.

Exercise 1.2.35 ($(a,a+2) = 1$ or $2$)

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Exercise 1.2.35 ($(a,a+2) = 1$ or $2$)

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