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equation $\frac{1}{2}=\sum_{i=1}^n\frac{1}{x_i^2}$

Source: 16-th Hungary-Israel Binational Mathematical Competition 2005

March 29, 2007
number theory unsolvednumber theory

Problem Statement

Find all sequences x1,x2,...,xnx_{1},x_{2},...,x_{n} of distinct positive integers such that 12=∑i=1n1xi2\frac{1}{2}=\sum_{i=1}^{n}\frac{1}{x_{i}^{2}}.
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