Integers and divisibility

(a) Show that $\gcd(n! + 1, (n + 1)! + 1) = 1$ for every $n\ge1$. (b) Show that if $\gcd(a, b) = 1$ then $\gcd(a + b, a - b)\in\{1, 2\}$. (c) Show that if $\gcd(a, b) = 1$ then $\gcd(a + b, ab) = 1$.