Question

if gcd(a,b) = 1, prove that gcd(a,b^2) = 1

Answer 1

Do you know Bezout's Identity?

Answer 2

Or rather, do you know this fact:

If a and b are integers and d=gcd(a,b), then there exists some integers x and y such that:\[ax+by=d\]

Basically this says the gcd of two numbers is some linear combination of the two numbers.

Answer 3

I squared both sides and was able to find the answer! Thank you so much!