Algebraic points on cubic hypersurfaces
Algebraically solvable problems: describing polynomials as equivalent to explicit solutions.
Algorithms for finding good examples for the and Szpiro conjectures.
All Congruent Numbers Less than 2000.
Almost perfect powers in arithmetic progression
Almost perfect powers in consecutive integers
Almost powers in the Lucas sequence
The famous problem of determining all perfect powers in the Fibonacci sequence and in the Lucas sequence has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations , with and , for all primes and indeed for all but primes . Here the strategy of [10] is not sufficient due to the sizes of...
Almost squares in arithmetic progression (II)
Amélioration de la majoration de g(4) dans le problème de Waring: g(4)≤30
An theorem over function fields and applications
We provide a lower bound for the number of distinct zeros of a sum for two rational functions , in term of the degree of , which is sharp whenever have few distinct zeros and poles compared to their degree. This sharpens the “-theorem” of Brownawell-Masser and Voloch in some cases which are sufficient to obtain new finiteness results on diophantine equations over function fields. For instance, we show that the Fermat-type surface contains only finitely many rational or elliptic curves,...
An additive divisor problem.
An Algorithm for a Linear Diophantine Equation and a Problem of Frobenius.
An algorithm for a solution of a problem of Frobenius.
An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture
An application of Hilbert's irreducibility theorem to diophantine equations
An arithmetic formula of Liouville
An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.
An arithmetical theorem on linear forms
An Artin Character and Represenattions of Primes by Binary Quadratic Forms.
An effective p-adic analogue of a theorem of Thue
An effective p-adic analogue of a theorem of Thue II. The greatest prime factor of a binary form