On the extension of the Diophantine pair in .
On the family of diophantine triples .
On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k
On the first case of Fermat's last theorem.
On the First Case of Fermat's Last Theorem, II.
On the Frobenius number of a modular Diophantine inequality
We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality , with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
On the Frobenius number of a proportionally modular Diophantine inequality.
On the Frobenius number of Fibonacci numerical semigroups.
On the Frobenius number of some Lucas numerical semigroups.
On the Frobenius problem for .
On the Frobenius problem for geometric sequences.
On the Galois groups of cubics and trinomials
On the generalized Fermat equation over totally real fields
In a recent paper, Freitas and Siksek proved an asymptotic version of Fermat’s Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form , where A, B, C are odd integers belonging to a totally real field.
On the generalized Ramanujan-Nagell equation I
On the generalized Ramanujan-Nagell equation, II
On the generalized Ramanujan-Nagell equation
On the greatest prime factor of
On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)
On the greatest prime factor of Markov pairs
On the integer solutions of exponential equations in function fields
This paper is concerned with the estimation of the number of integer solutions to exponential equations in several variables, over function fields. We develop a method which sometimes allows to replace known exponential bounds with polynomial ones. More generally, we prove a counting result (Thm. 1) on the integer points where given exponential terms become linearly dependent over the constant field. Several applications are given to equations (Cor. 1) and to the estimation of the number of equal...