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Which theorem states that a number N can't be perfectly divided by a number greater that N/2?

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    $\begingroup$ Why do you need a theorem? This can be simply proved using properties of inequality. $\endgroup$ Dec 15 '16 at 19:55
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    $\begingroup$ The same theorem which says that $N$ can not have a proper divisor $\lt 2$. $\endgroup$
    – dxiv
    Dec 15 '16 at 20:03
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Just think about it:

Suppose $M > N/2$. Then $2M > N$.

Thus, $M$ doesn't divide evenly into $N$ Because there is no number $a$ such that $aM = N$.

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Proposition: there are no integers $n$ such that $$ 1 < n < 2 $$

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    $\begingroup$ This gave me a good laugh. Thanks! $\endgroup$ Dec 15 '16 at 20:26

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