MathDB

Problem 1

Part of 2017 Mediterranean Mathematics Olympiad

Problems(1)

Equilateral triangle and constant function

Source:

6/15/2017
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.
geometry