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What is the the theorem or property that says that $\forall{}x\in\Bbb Z$, the set of all integers, $x^2$ has the same factors as $x$, twice?

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    $\begingroup$ ...I think you could imply it through the Fundamental Theorem of Arithmetic $\endgroup$ – daOnlyBG Apr 20 '15 at 1:29
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    $\begingroup$ Also known as, the Unique Factorization Theorem. $\endgroup$ – Gerry Myerson Apr 20 '15 at 7:06
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Well, the property may be the following: let $$ x={p_1}^{a_1}\cdot\ldots\cdot{p_n}^{a_n} $$ be the unique factorization of $x\in\Bbb Z$, $x>1$, then $$ x^2=\left({p_1}^{a_1}\cdot\ldots\cdot{p_n}^{a_n}\right)^2= {p_1}^{2a_1}\cdot\ldots\cdot{p_n}^{2a_n}. $$

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  • $\begingroup$ Thanks @shardulc for proofreading ;) $\endgroup$ – MattAllegro May 24 '15 at 16:31

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