MathDB
System of equations with a parameter

Source: 2023 Israel National Olympiad P4

December 16, 2022
algebrasystem of equationsparameterization

Problem Statement

For each positive integer nn, find all triples a,b,ca,b,c of real numbers for which {a=bn+cnb=cn+anc=an+bn\begin{cases}a=b^n+c^n\\ b=c^n+a^n\\ c=a^n+b^n\end{cases}
Back to ProblemsView on AoPS