On the torsion subgroups of elliptic curves over totally real fields.
On the two-dimensional theta functions of the Borweins
On the zeros of linear recurrence sequences
On Thue's equation.
On Thue's theorem.
On two theorems of Gelfond and some of their applications
On two-parametric family of quartic Thue equations
We show that for all integers and there are no non-trivial solutions of Thue equationsatisfying the additional condition .
On unit equations and decompsable form equations.
On unit equations with rational coefficients
On unit fractions with denominators in short intervals
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
On values of a polynomial at arithmetic progressions with equal products
On Waring's problem
On Waring's problem for two squares and three cubes.
On Wendt's determinant and Sophie Germain's theorem.
On Weyl's inequality and Waring's problem for cubes
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 .
On x³ + y³ + z³ = 3μxyz and Jacobi polynomials