0771
Source:
June 24, 2008
modular arithmeticquadraticsVietanumber theoryrelatively primealgebra
Problem Statement
Find all pairs of positive integers such that \begin{align*} b^2 + b+ 1 & \equiv 0 \pmod a \\ a^2+a+1 &\equiv 0 \pmod b . \end{align*}