On Rado conditions for nonlinear Diophantine equations

@article{Barrett2021OnRC,
title={On Rado conditions for nonlinear Diophantine equations},
author={Jordan Barrett and M. Lupini and Joel Moreira},
journal={Eur. J. Comb.},
year={2021},
volume={94},
pages={103277}
}

Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired by Rado's characterization of partition regular linear homogeneous equations. We conjecture that these conditions are also sufficient for partition regularity, at least for equations whose corresponding monovariate polynomial is linear. This would provide a natural generalization of Rado's theorem.
We verify that… Expand