On the two-colour Rado number for ${\sum }_{i=1}^m{a}_i{x}_i=c$

Ishan Arora, Srashti Dwivedi, Amitabha Tripathi

Let $a_1,\dots ,a_m$ be nonzero integers, $c\in \mathbb{Z}$ and $r\ge 2$. The Rado number for the equation \[ \sum_{i=1}^m a_ix_i = c \] in $r$ colours is the least positive integ…