MathDB

3

Part of 2022 Azerbaijan National Mathematical Olympiad

Problems(1)

set of positive integers such that 2x^2 + 3y^3 = 4z^4

Source: Thailand Mathematical Olympiad 2018 day 2 p6

1/20/2020
Let AA be the set of all triples (x,y,z)(x, y, z) of positive integers satisfying 2x2+3y3=4z42x^2 + 3y^3 = 4z^4 . a) Show that if (x,y,z)āˆˆA(x, y, z) \in A then 66 divides all of x,y,zx, y, z. b) Show that AA is an infinite set.
Diophantine equationdiophantinenumber theory