Given a prime number p and an integer n. Prove that gcd(n, n+p) is either 1 or p.
If p is less than n, then we have two cases: either n is a multiple of p, and then we'll get that the gcd is equal to p, or n is not a multiple of p, and then we'll get that the gcd is equal to 1.
However, if n is less than p, then we must get a 1 (we can't get p since p>n). I didn't figure out how to prove that! Need your help!