Families of curves having each an integer point
Fans and bundles in the graph of pairwise sums and products.
Hilbert's Tenth Problem for fields of rational functions over finite fields.
Linear equations in members of recurrence sequences
Linear forms in -adic logarithms. III
Northcott's Theorem on Heights I. A General Estimate.
Northcott's theorem on heights II. The quadratic case
O desátém Hilbertově problému
O riešení rovnice a rovnice v prirodzených číslach
On a problem of Erdős regarding binomial coefficients
On Diophantine quintuples
On mod logarithms and .
On the Brocard-Ramanujan problem and generalizations
Let denote the ith prime. We conjecture that there are precisely 28 solutions to the equation in positive integers n and α₁,..., . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).
On the Diophantine equation
On the Diophantine Equation tan (k .../m) = k tan .../m.
On the equation a(x...-1)/(x-1)=b(y...-1)/(y-1).
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...
On unit equations and decompsable form equations.
On unit equations with rational coefficients
Orthant spanning simplexes with minimal volume.