The difference between the arithmetic mean and the geometric mean of two positive integers and is 1. Prove that and are perfect squares.

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- Oct 22nd 2008, 02:22 AMalexmahoneArithmetic mean and Geometric mean
The difference between the arithmetic mean and the geometric mean of two positive integers and is 1. Prove that and are perfect squares.

- Oct 22nd 2008, 02:50 AMSimonM

Clearly is a perfect square, therefore for some square free t

Therefore

as required