Finitely many 'good' numbers

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Phlembac Adib Hasan
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Finitely many 'good' numbers

Unread post by Phlembac Adib Hasan » Mon Nov 07, 2016 11:55 am

For a positive integer $n$, denote by $\tau (n)$ the number of its positive divisors. For a positive integer $n$, if $\tau(m) < \tau(n)$ for all positive integers $m<n$, we call $n$ a good number. Prove that for any positive integer $k$, there are only finitely many good numbers not divisible by $k$.
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