85 citations · 87 across the 2 of their papers we have counts for
5 papers
Two-cover descent on hyperelliptic curves
Nils Bruin, Michael Stoll
We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In par…
Deciding existence of rational points on curves: an experiment
Nils Bruin, Michael Stoll
We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For e…
Arithmetic progressions consisting of unlike powers
N. Bruin, K. Gyory, L. Hajdu +1
In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given and there are only finitely…
The arithmetic of Prym varieties in genus 3
Nils Bruin
Given a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym-variety. We also describe how an unramified double cover of a non-h…
The primitive solutions to x^3+y^9=z^2
Nils Bruin
We determine the rational integers x,y,z such that x^3+y^9=z^2 and gcd(x,y,z)=1. First we determine a finite set of curves of genus 10 such that any primitive solution to x^3+y^9=z…