Sur une question de V. A. Lebesgue. (On a question of V. A. Lebesgue). (French) Zbl 0616.10013

We prove a conjecture of V. A. Lebesgue on the diophantine equation \(x^ 4+x^ 3y+x^ 2y^ 2+xy^ 3+y^ 4=5z^ 5\) using elementary arguments which lead us to the solution of some other equations.


11D41 Higher degree equations; Fermat’s equation
11D25 Cubic and quartic Diophantine equations
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[1] [1] , Théorèmes nouveaux sur l’équation indéterminée x5 + y5 = a z5, Journal de Mathématiques, 8 (1843), 49-70.
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