MathDB

Cubic diophantine equation solving algorithm

Source: Kazakhstan National 2021, Problem 5

April 28, 2021

KazakhstanDiophantine equationnumber theory proposedalgebranumber theory

Problem Statement

Let

a

be a positive integer. Prove that for any pair

(x,y)

of integer solutions of equation

x(y^2-2x^2)+x+y+a=0

we have:

|x| \leqslant a+\sqrt{2a^2+2}