proof-or-given-a-counter-example-if-n-2-is-prime-then-n-Z-

Question Number 471 by 123456 last updated on 25/Jan/15

p r o o f o r g i v e n a c o u n t e r e x a m p l e :

i f n^{2} i s p r i m e, t h e n n \notin Z

Answered by prakash jain last updated on 10/Jan/15

n^{2} is prime so n^{2} > 1 .

If n \in Z, n > 1 or n < - 1

and ∣ n ∣ divides n^{2} which will make n^{2} composite

which contraticts n^{2} is prime .