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.
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Davide Giraudo
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1Hint: Use contrapositive. – Jacky Chong Oct 28 '16 at 05:50
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@JackyChong..it mean suppose x is positive the $x^2$ is not prime – Oct 28 '16 at 05:54
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Yes. Now prove the statement. – Jacky Chong Oct 28 '16 at 05:55
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@JackyChong..how we start suppose $x^2$ is prime then how go next.. – Oct 28 '16 at 06:01
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You should start by assuming $x$ is a positive integer. – Jacky Chong Oct 28 '16 at 06:02
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@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
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@JackyChong..coz we cant be expressed as a prime is power of square – Oct 28 '16 at 06:06
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Let us continue this discussion in chat. – Oct 28 '16 at 06:11
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@JackyChong...can you tell is am right are wrong – Oct 28 '16 at 06:11
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http://math.stackexchange.com/questions/979211/the-square-root-of-a-prime-number-is-irrational – Soham Oct 28 '16 at 07:07
1 Answers
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Hint: obviously $$x|x^2.$$ But $x^2$ is prime, thus its only (integer) divisors are $1$ and $x^2$. Conclude
b00n heT
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