MathDB
f(M)=MA^n+MB^n+MC^n

Source: Moldova TST 2021

September 20, 2021
functionalgebrageometry

Problem Statement

Let ABCABC be an equilateral triangle. Find all positive integers nn, for which the function ff, defined on all points MM from the circle SS circumscribed to triangle ABCABC, defined by the formula f:Sā†’R,f(M)=MAn+MBn+MCnf:S \rightarrow R, f(M)=MA^n+MB^n+MC^n, is a constant function.
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