the possible values of gcd(a; a + prime).

**zhushp** · November 7th 2009, 10:49 PM

If p is a prime, find the possible values of gcd(a, a + p).

and find a necessary and sufficient condition for gcd(a, a+p) = 1 where p is a
prime.

**Bruno J.** · November 8th 2009, 12:27 AM

If $d$ divides both $a$ and $a+p$ then $d|p$ , so $d=1$ or $d=p$ .

A necessary and sufficient condition that $\mbox{gcd }(a,a+p)=1$ is that $p\nmid a$ .

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