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Nous démontrons une conjecture de V.A. Lebesgue relative à l’équation diophantienne $x^{4} + x^{3} y + x^{2} y^{2} + x y^{2} + y^{4} = 5 z^{5}$ par une méthode élémentaire qui fournit également la solution de quelques autres équations.

Symmetric Diophantine systems

Ajai Choudhry (1991)

Acta Arithmetica

Symmetric diophantine systems revisited

Ajai Choudhry (2005)

Acta Arithmetica

Systems of Homogeneous Equations.

D.B. Leep, W.M. Schmidt (1983)

Inventiones mathematicae

The Brauer-Manin obstruction on a general diagonal quartic surface

Martin Bright (2011)

Acta Arithmetica

The cubic congruence $x^{3} + a x^{2} + b x + c \equiv 0 (mod p)$ and binary quadratic forms $F (x, y) = a x^{2} + b x y + c y^{2}$ . II.

Tekcan, Ahmet (2010)

Acta Universitatis Apulensis. Mathematics - Informatics

The density of rational points on cubic surfaces

D. R. Heath-Brown (1997)

Acta Arithmetica

The Diophantine Equation ...

L.J. Mordell (1967)

Mathematische Annalen

The diophantine equation $d y^{2} = a x^{4} + b x^{2} + c$

L. Mordell (1969)

Acta Arithmetica

The diophantine equation $n^{i} + 1 = k (d n - 1)$ .

Ligh, Steve, Bourque, Keith (1989)

International Journal of Mathematics and Mathematical Sciences

The Diophantine equation $x^{4} - y^{4} = z^{2}$ in three quadratic fields.

Szabó, Sándor (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

The diophantine equation (x2 - 1) (y2 - 1) = (z2 - 1)2: a footnote.

Shoichi Hirose (1987)

Elemente der Mathematik

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