Counting Square-full Solutions to $x+y=z$
Number Theory
2026-01-13 v1
Abstract
We show that there are triples of square-full integesr up to satisfying the equation for any fixed . This is the first improvement over the `easy' exponent , given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations .
Keywords
Cite
@article{arxiv.2601.07817,
title = {Counting Square-full Solutions to $x+y=z$},
author = {D. R. Heath-Brown},
journal= {arXiv preprint arXiv:2601.07817},
year = {2026}
}