On the Kummer-Mirimanoff congruences
On the Lebesgue-Nagell equation
We completely solve the Diophantine equations (for q = 17, 29, 41). We also determine all and , where are fixed primes satisfying certain conditions. The corresponding Diophantine equations x² + C = yⁿ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).
On the method of Coleman and Chabauty.
On the number of rational squares at fixed distance from a fifth power
On the Number of S-Integral Solutions to Ym = f(x).
On the Product of Consecutive Elements of an Arithmetic Progression.
On the relation between two conjectures on polynomials
On the relation between units and Jacobi sums in Prime cyclotomic Fields.
On the solutions of diophantine equations in units
On the Thue-Mahler equation II
On Thue's equation.
On unit equations and decompsable form equations.
On Wendt's determinant and Sophie Germain's theorem.
On and
The two related Diophantine equations: and , have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations.
On
In p. 219 of R.K. Guy’s Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation has no integer solutions with and . But, contrary to this expectation, we show that for , this equation has infinitely many primitive integer solutions, i.e. the solutions satisfying the condition .
Osservazioni sul problema di Fermat.