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sum |PA|^n + |PB|^n + |PC|^n + |PD|^n is constant wrt point P

Source: Indian Postal Coaching 2007 set 3 p1

May 25, 2020
Sumgeometryconstantcircumcirclesquare

Problem Statement

Let PP be a point on the circumcircle of a square ABCDABCD. Find all integers n>0n > 0 such that the sum Sn(P)=∣PA∣n+∣PB∣n+∣PC∣n+∣PD∣nS_n(P) = |PA|^n + |PB|^n + |PC|^n + |PD|^n is constant with respect to the point PP.
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