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Solving (x+2)^4-x^4=y^3 over the integers

Source: Bundeswettbewerb Mathematik 2024, Round 2 - Problem 1

September 13, 2024

number theorynumber theory proposedDiophantine equation

Problem Statement

Determine all pairs

(x,y)

of integers satisfying

(x+2)^4-x^4=y^3.