Find all n
Source: From Kazakhstan National Olympiad 2003
February 15, 2008
number theory proposednumber theory
Problem Statement
Find all natural numbers ,such that there exist x_1,x_2,\dots,x_{n\plus{}1}\in\mathbb{N},such that
\frac{1}{x_1^2}\plus{}\frac{1}{x_2^2}\plus{}\dots\plus{}\frac{1}{x_n^2}\equal{}\frac{n\plus{}1}{x_{n\plus{}1}^2}.