Some diophantine equations solvable by identities
Some fourth degree Diophantine equations in Gaussian integers.
Some observations on the Diophantine equation f(x)f(y) = f(z)²
Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.
Some simple elliptic surfaces of genus zero.
Some special curves of genus 5
Square-classes in Lehmer sequences having odd parameters and their applications
Squares in arithmetical progressions I.
Squares in arithmetical progressions II.
Squares in Lehmer sequences and some Diophantine applications
Squares in Lehmer sequences and the Diophantine equation Ax⁴ - By² = 2
Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan]
Sur des équations diophantiennes généralisant celle de Markoff
Sur la monogeneite de l'anneau des entiers de certains corps de rayon.
Sur l'analyse indéterminée du troisième degré et sur la question 802 (Sylvester)
Sur l'équation diophantienne (x2-1) (y2-1) = [(...)2 -1]2.
Sur l'équation diophantienne (x2-1)2 + (y2-1)2 = (z2-1)2.
Sur l’équation diophantienne
Sur l’équation indéterminée biquadratique
Sur l’équation indéterminée
Sur l’équation