Problem

Source: 2021 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand

Tags: number theory, Diophantine equation, diophantine



A triplet of positive integers $(x, y, z)$ satisfying $x, y, z > 1$ and $x^3 - yz^3 = 2021$ is called primary if at least two of the integers $x, y, z$ are prime numbers. a) Find at least one primary triplet. b) Show that there are infinitely many primary triplets.