Difference between revisions of "2007 iTest Problems/Problem 44"

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Revision as of 23:01, 7 October 2014

Problem

A positive integer $n$ between $1$ and $N=2007^{2007}$ inclusive is selected at random. If $a$ and $b$ are natural numbers such that $a/b$ is the probability that $N$ and $n^3-36n$ are relatively prime, find the value of $a+b$.

Solution