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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111661Euler 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.``Solutio problematis Fermatiani de duobus numeris, quorum summa sit quadratum, quadratorum vero summa biquadratum, ad mentem illustris La Grange adornata'', Memoires de l'Academie Imperiale des Sciences de St.-Petersbourg 10 (1826), 3-6. E769 in the Enestrom indexHistory and OverviewNumber Theory01A50; 11D09A 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 Grangetext