MathDB

7.1

Part of MathLinks Contest 7th

Problems(1)

0771

Source:

6/24/2008
Find all pairs of positive integers a,b a,b such that \begin{align*} b^2 + b+ 1 & \equiv 0 \pmod a \\ a^2+a+1 &\equiv 0 \pmod b . \end{align*}
modular arithmeticquadraticsVietanumber theoryrelatively primealgebra