# Math Help - Abstract algebra proof

1. ## Abstract algebra proof

If $a$ and $b$ are natural numbers, $(a,b) = 1$, and $ab$ is square, show that $a$ and $b$ are squares.

2. Originally Posted by Zennie
If $a$ and $b$ are natural numbers, $(a,b) = 1$, and $ab$ is square, show that $a$ and $b$ 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.