MathDB

a - b and 2a + 2b + 1 are squares of integers if 2a^2 + a = 3b^2 + b

Source: Polish MO Finals 1965 p4

August 30, 2024

number theoryPerfect Square

Problem Statement

Prove that if the integers

a

and

b

satisfy the equation

2a^2 + a = 3b^2 + b,

then the numbers

a - b

and

2a + 2b + 1

are squares of integers.