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Equilateral triangle and constant function

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June 15, 2017
geometry

Problem Statement

Let ABCABC be an equilateral triangle, and let PP be some point in its circumcircle. Determine all positive integers nn, for which the value of the sum Sn(P)=∣PA∣n+∣PB∣n+∣PC∣nS_n (P) = |PA|^n + |PB|^n + |PC|^n is independent of the choice of point PP.
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