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A solution to a problem of Fermat, on two numbers of which the sum is a square and the sum of their squares is a biquadrate, inspired by the Illustrious La Grange

Research paper by Leonhard Euler

Indexed on: 23 Apr '06Published on: 23 Apr '06Published in: Mathematics - History and Overview



Abstract

Euler wants to find rational numbers (integers) x and y such that x+y is a square and x^2+y^2 is a fourth power. He parametrizes these with two other variables that satisfy certain equations.