Rado's criterion over higher powers.

Sean Prendiville (University of Manchester)

Frank Adams 1,

In Ramsey theory, Schur's theorem states that however one colours the positive integers with finitely many colours, there always exists a solution to the equation x+y = z in which each variable receives the same colour. Rado completely characterised which linear equations possess this property and which do not. We discuss analogues of these results for certain non-linear Diophantine equations.

This is joint with with Sam Chow (York) and Sofia Lindqvist (Oxford).
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