4

Part of 2024 Greece National Olympiad

Problems(1)

Diophantine equation has too many solutions for some n

Source: Greece National Olympiad 2024, Problem 4

Prove that there exists an integer

n \geq 1

, such that number of all pairs

(a, b)

of positive integers, satisfying

\frac{1}{a-b}-\frac{1}{a}+\frac{1}{b}=\frac{1}{n}

2024.