On Powers as Sums of Two Cubes. - Nils Bruin (ANTS, 2000)

Trinomials ax and ax with Galois Groups of Order 168 and 8·168. - Nils Bruin; Noam D. Elkies (ANTS, 2002)

Rational Divisors in Rational Divisor Classes. - Nils Bruin; E. Victor Flynn (ANTS, 2004)

Visualising Sha[2] in Abelian surfaces. - Nils Bruin (Math. Comput., 2004)

The Brauer-Manin Obstruction and III[2]. - M. J. Bright; Nils Bruin; E. Victor Flynn; A. Logan (LMS J. Comput. Math., 2007)

Deciding Existence of Rational Points on Curves: An Experiment. - Nils Bruin; Michael Stoll (Exp. Math., 2008)

Two-cover descent on hyperelliptic curves. - Nils Bruin; Michael Stoll (Math. Comput., 2009)

Visualizing Elements of Sha[3] in Genus 2 Jacobians. - Nils Bruin; Sander R. Dahmen (ANTS, 2010)

The Mordell-Weil sieve: proving non-existence of rational points on curves. - Nils Bruin; Michael Stoll (LMS J. Comput. Math., 2010)

Minimal models for rational functions in a dynamical setting. - Nils Bruin; Alexander Molnar (LMS J. Comput. Math., 2012)

Arithmetic aspects of the Burkhardt quartic threefold. - Nils Bruin; Brett Nasserden (J. Lond. Math. Soc., 2018)

Rigorous numerical integration of algebraic functions. - Nils Bruin; Linden Disney-Hogg; Wuqian Effie Gao (CoRR, 2022)