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Let $p$ and $q$ be distinct primes. Show that the equation $\textrm{lcm}(a, b) = (p^2) q$ has fifteen solutions in positive integers $a, b$.

Thanks for any help in advance as I don't know how to proceed with this question.

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  • $\begingroup$ Hello, and welcome to MSE. To help get people to answer your question, plus avoid down-voting and getting your question closed, please tell us what you've tried so far, including anything you've had difficulty with. Thanks. $\endgroup$ – John Omielan Feb 18 at 3:34
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    $\begingroup$ Also, please use MathJax $\endgroup$ – J. W. Tanner Feb 18 at 3:44
  • $\begingroup$ I can add MathJax for you, seeing that you're new. But I can't add what you've tried so far since I don't know what that is. $\endgroup$ – Robert Soupe Feb 18 at 4:29
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Hint: What are the divisors of $p^2 q$?

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