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2017 Polish Junior Math Olympiad Finals P3

Source: 2017 Polish Junior Math Olympiad Finals

May 22, 2023

number theory

Problem Statement

Positive integers

a

and

b

are given such that each of the numbers

ab

and

(a+1)(b+1)

is a perfect square. Prove that there exists an integer

n>1

such that the number

(a+n)(b+n)

is a perfect square.