Question

Prove that if a and b are coprime, then a^2 + b^2 are as well coprime.

Answer 1

a^2+b^2 is a number, what is it coprime to?

Answer 2

I think you mean \((a^2,b^2)=1\)

Suppose \((a,b)=1\) and suppose to the contrary that \((a^2,b^2)=k\) for some \(k\) is prime. Then \(k|a^2\) and \(k|b^2\) then use Euclid's lemma.

Answer 3

Yea as it stands the statement makes no sense

a^2, b^2 are coprime sounds a lot better