Agnieszka Peszek

most citedIs there a computable upper bound on the heights of rational solutions of a Diophantine equation with a finite number of solutions?

2 citations · 3 across the 2 of their papers we have counts for

collaborators

2 papers

math.LO2019★ 1 cited

Hilbert's 10th Problem for solutions in a subring of Q

Agnieszka Peszek, Apoloniusz Tyszka

Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that…

math.NT2015★ 2 cited

Is there a computable upper bound on the heights of rational solutions of a Diophantine equation with a finite number of solutions?

Apoloniusz Tyszka

The height of a rational number $p / q$ is denoted by $h (p / q)$ and equals $max (∣ p ∣, ∣ q ∣)$ provided p/q is written in lowest terms. The height of a rational tuple $(x_1,...,x_n)…