MathDB

x-y,2x + 2y + 1,3x + 3y + 1 are pefrect squares if 2x^2 + x = 3y^2 + y

Source: 1988 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1

November 20, 2022

number theoryPerfect SquaresPerfect Square

Problem Statement

For the natural numbers

x

and

y

2x^2 + x = 3y^2 + y

. Prove that then

x-y

2x + 2y + 1

and

3x + 3y + 1

are perfect squares.