Thread: Abstract algebra proof

If and are natural numbers, , and is square, show that and are squares.

Originally Posted by Zennie

If and are natural numbers, , and is square, show that and are squares.

ab has a unique prime number decomposition. Since ab is even, every prime number is to an even power. Now look at the prime number decompositions of a and b. Since (a,b)= 1, they have NO prime numbers in common.