BG-JBMO-TST 2022 Problem 1

Are there positive integers $a$ , $b$ , $c$ and $d$ such that:

a) $a^{2021} + b^{2023} = 11(c^{2022} + d^{2024})$ ;

b) $a^{2022} + b^{2022} = 11(c^{2022} + d^{2022})$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.