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March 19th, 2017, 11:32 AM   #1
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Unhappy if n|x^2 then n|x

1)if n is a positive integer and doesn't have a factor of any positive integer except 1
2)if x is an integer
then,
how to prove that if n|x^2 then n|x?
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March 19th, 2017, 01:17 PM   #2
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1) You presumably mean "doesn't have a factor of any positive integer except $n$ and $1$". $n$ is prime, so you are going to refer to the prime factorisation of numbers, in particular that a prime factorisation is unique up to the order of the factors.

2) You might find it easier to prove the contra-positive: if $n$ does not divide $x$ then $n$ does not divide $x^2$. The two results are equivalent.
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March 19th, 2017, 01:29 PM   #3
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what if n can has factors of positive integers but not square factors?
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March 19th, 2017, 04:12 PM   #4
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$n$ is prime by the definition you gave.
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