a^6 + 1 | b^{11} - 2023b^3 + 40b and a^4 - 1 | b^{10} - 2023b^2 - 41
Source: 2023 Abelkonkurransen Finale, Problem 3b
March 12, 2024
number theoryDivisibility
Problem Statement
Find all integers and satisfying
\begin{align*}
a^6 + 1 & \mid b^{11} - 2023b^3 + 40b, \qquad \text{and}\\
a^4 - 1 & \mid b^{10} - 2023b^2 - 41.
\end{align*}