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Squares in P_n - JBMO Shortlist

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October 30, 2010
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let Pn (n=3,4,5,6,7)P_n \ (n=3,4,5,6,7) be the set of positive integers nk+nl+nmn^k+n^l+n^m, where k,l,mk,l,m are positive integers. Find nn such that:
i) In the set PnP_n there are infinitely many squares.
ii) In the set PnP_n there are no squares.
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