proof-or-give-a-counter-example-if-nm-is-prime-then-mdc-n-2-m-2-1-

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