arXiv subjects

Sz. Tengely

Publications and source records attributed to Sz. Tengely.

3 recordsLinked to original sources

arXiv2010

Integral Points on Hyperelliptic Curves

We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement of the Mordell--Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on a two genus 2 hyperelliptic curves with Mordell--Weil Jacobian ranks of 3 and 6.

math.NT↗

arXiv2005

An implementation of Runge's method for Diophantine equations

In this paper we suggest an implementation of Runge's method for solving Diophantine equations satisfying Runge's condition. In this implementation we avoid the use of Puiseux series and algebraic coefficients.

math.NT↗

arXiv2005

Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.

math.NT↗