# 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

#### 3 Citations

#### References

SHOWING 1-10 OF 38 REFERENCES

New polynomial and multidimensional extensions of classical partition results

- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 2017

Density and ramsey type results on algebraic equations with restricted solution sets

- Mathematics, Computer Science
- Comb.
- 2012

On the Number of Monochromatic Solutions of ${\bm x}+{\bm y}={\bm z}^{{\bm 2}}$

- Mathematics, Computer Science
- Combinatorics, Probability and Computing
- 2006

Partition Regularity of Nonlinear Polynomials: A Nonstandard Approach

- Mathematics, Computer Science
- Integers
- 2014

Ergodic theorem involving additive and multiplicative groups of a field and $\{x+y,xy\}$ patterns

- Mathematics
- Ergodic Theory and Dynamical Systems
- 2015