Hi, I need opinion about this problem. ================================================== question :Prove: If(a,b)= l and if ( "(a,b)=1" mean greatest common divisor of integers and b is 1 ) c|a (c divides a) and d|b (d divides b ) then (c,d)= 1. ( "(c,d)=1" mean greatest common divisor of integers and b is 1 ) <-- this need to be proved. ======================================== (Is that following a good proof ?) ======================================== Then there are 2 sets A and B. divisors of a ∈ A <-- do this need be proved too? divisors of b ∈ B A ∩ B = 1 since c ⊂ A d ⊂ B c ∩ b = 1 which is what we are looking for. =========================================== Thank you.