Romania NMO 2023 Grade 6 P2
Source: Romania National Olympiad 2023
April 14, 2023
algebraequationnumber theory
Problem Statement
Determine all triples of integers that simultaneously satisfy the following relations: \begin{align*}
a^2 + a = b + c, \\
b^2 + b = a + c, \\
c^2 + c = a + b.
\end{align*}