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

2006/04/23 by Leonhard Euler, Euler, Leonhard
Mathematics · #01A50 #11D09 #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0604496

openalex publication_date 2006/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Euler wants to find rational numbers (integers) x and y such that x+y is a square and x²+y² is a fourth power. He parametrizes these with two other variables that satisfy certain equations.

Related

• Square Eulerian Quadruples
• Extended Lagrange's four-square theorem
• The problem of finding three numbers such that the sum or difference of any two of them is a square number
• Observations on two fourth powers whose sum is equal to the sum of two other fourth powers
• Sums of four rational squares with certain restrictions