If $x^2$ is prime, then x is not a positive integer

Question

Prove the following statement using a technique (contrapositive or contradiction)

If $x^2$ is prime, then $x$ is not a positive integer

My attempt: suppose $X$ is positive integer for further I can't get any idea any one help.

@JackyChong..it mean suppose x is positive the $x^2$ is not prime — , Oct 28 '16 at 05:54
@JackyChong..how we start suppose $x^2$ is prime then how go next.. — , Oct 28 '16 at 06:01
@JackyChong...suppose x is positive integer then $x^2 $ is positive integer ..then Is we can say directly x^2 is not prime — , Oct 28 '16 at 06:04
@JackyChong..coz we cant be expressed as a prime is power of square — , Oct 28 '16 at 06:06
http://math.stackexchange.com/questions/979211/the-square-root-of-a-prime-number-is-irrational — Soham, Oct 28 '16 at 07:07

score 1 · Answer 1 · answered Oct 28 '16 at 07:04

1

Hint: obviously $$x|x^2.$$ But $x^2$ is prime, thus its only (integer) divisors are $1$ and $x^2$. Conclude

answered Oct 28 '16 at 07:04

b00n heT

1 Answers1