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Let $x=2^6 3^4 5^2$, then how many distinct values of $|A-B|$ are possible where $A, B$ are the factors of $x$?

How to approach this problem?

  • 0
    Where did this problem come from? What have you tried so far? It's easy to establish an upper bound on the number of distinct values (how many factors of $x$ are there? If $N$ is the number of factors, how many ordered pairs of numbers $\lt N$ are there?), but 'coincidences' where two distinct pairs of factors $\langle A,B\rangle$ and $\langle C,D\rangle$ have the same difference can happen, and there's no immediately obvious way of tallying the coincidences except going through all the possibilities by hand.2012-07-23
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    Are you sure you aren't being asked to tally how many distinct values of $|A-B|$ are possible where $AB=x$? That would be a different (and much more easily manageable by hand) problem...2012-07-23
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    No, $AB$ doesn't necessarily equal to $x$.2012-07-23

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