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Find all m that P_m is divisible by 33^33

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August 30, 2010
number theoryDivisibilityIMO ShortlistIMO Longlist

Problem Statement

Let Pn=(19+92)(192+922)⋯(19n+92n)P_n = (19 + 92)(19^2 +92^2) \cdots(19^n +92^n) for each positive integer nn. Determine, with proof, the least positive integer mm, if it exists, for which PmP_m is divisible by 3333.33^{33}.
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