proof or give a counter−example: if nm is prime then mdc(n^2 ,m^2 )=1


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Question Number 472 by 123456 last updated on 25/Jan/15

$p r o o f o r g i v e a c o u n t e r - e x a m p l e :$ $i f n m i s p r i m e t h e n mdc (n^{2}, m^{2}) = 1$
	Answered by prakash jain last updated on 10/Jan/15

	$If n, m \in Z then n = 1 or m = 1$ $and \gcd (n^{2}, m^{2}) = 1$ $For general case counter example$ $n = \sqrt{3}, m = \sqrt{3}$ $n m = 3 (prime)$ $\gcd (n^{2}, m^{2}) = \gcd (3, 3) = 3$
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