Thursday 15 Mar 2018: Number Theory Seminar: Rado's criterion over squares and higher powers
Sofia Lindqvist - University of Oxford
An equation is said to be partition regular if any finite colouring of the integers has a monochromatic solution, i.e. a solution where all variables receive the same colour. A classical result of Rado fully characterises which linear equations are partition regular. We give analogues of this result for sums of k'th powers, provided the number of variables is large enough in terms of k. This is joint work with Sam Chow and Sean Prendiville.