Terjanian, Guy Sur une question de V. A. Lebesgue. (On a question of V. A. Lebesgue). (French) Zbl 0616.10013 Ann. Inst. Fourier 37, No. 3, 19-37 (1987). 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. MSC: 11D41 Higher degree equations; Fermat’s equation 11D25 Cubic and quartic Diophantine equations Keywords:quintic diophantine equation; eight order; quartic diophantine equation PDF BibTeX XML Cite \textit{G. Terjanian}, Ann. Inst. Fourier 37, No. 3, 19--37 (1987; Zbl 0616.10013) Full Text: DOI Numdam EuDML OpenURL References: [1] V.A. LEBESGUE, Théorèmes nouveaux sur l’équation indéterminée x5 + y5 = a z5, Journal de Mathématiques, 8 (1843), 49-70. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.