The representation of primes by quadratic and cubic polynomials
The resolution of the diophantine equation x(x+d)...(x+(k-1)d) = by² for fixed d
The set of solutions of a polynomial-exponential equation
The simultaneous Pell equations y²-Dz² = 1 and x²-2Dz² = 1
The size of Selmer groups for the congruent number problem.
The size of the fundamental solutions of consecutive Pell equations.
The solubility of diagonal cubic surfaces
The solvability of the diophantine equation
The subspace theorem and applications.
The Tarry-Escott and the "easier" Waring problems.
The terms in Lucas sequences: an algorithm and applications to diophantine equations
The unit equation and the cluster principle
The value of additive forms at prime arguments
Let be an additive form of degree with prime variables . Suppose that has real coefficients with at least one ratio algebraic and irrational. If s is large enough then takes values close to almost all members of any well-spaced sequence. This complements earlier work of Brüdern, Cook and Perelli (linear forms) and Cook and Fox (quadratic forms). The result is based on Hua’s Lemma and, for , Heath-Brown’s improvement on Hua’s Lemma.
The Way to the Proof of Fermat’s Last Theorem
The zero-multiplicity of ternary recurrences
Théorème de Brun-Titchmarsh; application au théorème der Fermat.
Théorème de Fermat : la contribution de Fouvry
Théorème de Terjanian généralisé
En 1977 G. Terjanian étonna tous les spécialistes du théorème de Fermat en prouvant le premier cas... pour les exposants pairs. Nous généralisons ici cette propriété dans le cas des corps de nombres de degré impair et ayant un nombre impair de classes d'idéaux.
Théorème d'irréductibilité de Hilbert effectif
Théorème sur la géométrie des quinconces