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Part of 2021 Grand Duchy of Lithuania

Problems(1)

diophantine x^3 - yz^3 = 2021 with at least 2 primes

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

10/30/2021
A triplet of positive integers (x,y,z)(x, y, z) satisfying x,y,z>1x, y, z > 1 and x3āˆ’yz3=2021x^3 - yz^3 = 2021 is called primary if at least two of the integers x,y,zx, y, z are prime numbers. a) Find at least one primary triplet. b) Show that there are infinitely many primary triplets.
number theoryDiophantine equationdiophantine