Sums-of-Two-Sixth-Powers

This is the repository that contains all of the code used in the paper "Integers that are sums of two rational sixth powers" by Alexis Newton and Jeremy Rouse.

The authors can be contacted at alexis.newton@emory.edu and rouseja@wfu.edu, respectively.

The paper can be found on the arXiv here: https://arxiv.org/abs/2101.09390

This work represents joint work done when the first author was a master’s student at Wake Forest University. Computations were done in Magma version 2.26-9 on a desktop with an Intel i9-11900K CPU and 128 GB of RAM.

All the steps combine to form a proof that 164634913 is the smallest integer that is a sum of two rational sixth powers but not a sum of two integer sixth powers.