On the Diophantine equation
On the diophantine equations
On the Frobenius problem for geometric sequences.
On the numbers that are representable as the sum of two cubes.
On the representation of a number in the form x^2+y^2+p^2+q^2 where p, q are odd primes
On the Representation of Integers by Binary Cubic Forms of Positive Discriminant.
On the representation of integers by binary cubic forms of positive discriminant (Erratum).
On the representations of .
On the sum of consecutive cubes being a perfect square
On Waring's problem
On Waring's problem for two squares and three cubes.
On Weyl's inequality and Waring's problem for cubes
Original title unknown
Parametrization of integral values of polynomials
We will recall a recent result about the classification of those polynomial in one variable with rational coefficients whose image over the integer is equal to the image of an integer coefficients polynomial in possibly many variables. These set is polynomially generated over the integers by a family of polynomials whose denominator is and they have a symmetry with respect to a particular axis.We will also give a description of the linear factors of the bivariate separated polynomial over a...
Primes represented by quadratic polynomials in two variables
Problème de Waring avec exposant non entier
Problème de Waring avec exposants non entiers
Problème de Waring pour les bicarrés : le point en 1984
Pythagorean primes and palindromic continued fractions.
Rational solutions of certain Diophantine equations involving norms
We present some results concerning the unirationality of the algebraic variety given by the equation , where k is a number field, K=k(α), α is a root of an irreducible polynomial h(x) = x³ + ax + b ∈ k[x] and f ∈ k[t]. We are mainly interested in the case of pure cubic extensions, i.e. a = 0 and b ∈ k∖k³. We prove that if deg f = 4 and contains a k-rational point (x₀,y₀,z₀,t₀) with f(t₀)≠0, then is k-unirational. A similar result is proved for a broad family of quintic polynomials f satisfying...