Partition Regularity for Systems of Diagonal Equations

Research output: Contribution to journalArticle (Academic Journal)peer-review


We consider systems of $n$ diagonal equations in $k$th powers. Our main result shows that if the coefficient matrix of such a system is sufficiently nonsingular, then the system is partition regular if and only if it satisfies Rado’s columns condition. Furthermore, if the system also admits constant solutions, then we prove that the system has nontrivial solutions over every set of integers of positive upper density.
Original languageEnglish
JournalInternational Mathematics Research Notices
Early online date11 May 2021
Publication statusE-pub ahead of print - 11 May 2021


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