Prove or disprove: if $n\mid x^2$ and $n<x$, then $n\mid x$.
I am having trouble finding a convincing proof. I have only examples that show it is true. Can someone please give me hints or solutions?
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Diego Artacho
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Ray
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2If $x<n$, then $n$ never divides $x$ (we are working with positive integers here). – Diego Artacho Mar 16 '22 at 12:19
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sorry, I think itis n<x not x<n. Can I change the title – Ray Mar 16 '22 at 12:20
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Yes, you can edit your post. – lulu Mar 16 '22 at 12:22
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3Note that $9,|,12^2$. – lulu Mar 16 '22 at 12:23
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@lulu Ah ok found a counterexample. I think this question is answered now. – Ray Mar 16 '22 at 12:24
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4$4\mid 6^2$ but $4\nmid 6$ is a smaller counterexample (smallest if you don't include negative numbers) – JMoravitz Mar 16 '22 at 12:26