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

Source: Thailand Mathematical Olympiad 2018 day 2 p6

January 20, 2020

Diophantine equationdiophantinenumber theory

Problem Statement

Let

A

be the set of all triples

(x, y, z)

of positive integers satisfying

2x^2 + 3y^3 = 4z^4

. a) Show that if

(x, y, z) \in A

then

6

divides all of

x, y, z

. b) Show that

A

is an infinite set.