Partition regularity and non-linear Diophantine equations
Heilbronn Number Theory Seminar
30th May 2018, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
Schur's theorem states that however one finitely colours the positive integers, there is always 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 in sufficiently many variables.