Rado equations solved by linear combinations of idempotent ultrafilters

Abstract

We fully characterise the solvability of Rado equations inside linear combinations $a_{1}\U\oplus\dots\oplus a_{n}\U$ of idempotent ultrafilters $\U\in\beta\Z$ by exploiting known relations between such combinations and strings of integers. This generalises a partial characterization previously obtained by Mauro Di Nasso.