OK: "Prove that, for a positive integer n and any integer a, gcd(a, a+n) divides n; hence, gcd(a, a+1) = 1."
starters: "HENCE"??? is that essentially the "therefore, by the given gcd(a, a+n) divides n, then gcd(a, a+1) must equal 1"???
Or are we supposed to prove the gcd(a, a+n) part?
Either way, where do I start?