Are the following true or false? Prove the true statements and provide a counter example for the false ones (a and b are positive integers and p

is prime):

(a) ifgcd(a,b) =pthen gcd(a2,bp) =p2;

(b) if gcd(a,p2) = p and gcd(b,p2) = p2 then gcd(ab,p4) = p3 ;

(c) if gcd

(a, b) = p then gcd(a2 , ab) = p2 ;

(d) if a2 + b2 = p2 then gcd

(a, b) = 1.