The Chevalley-Warning theorem
and a combinatorial question on finite groups
Abstract: Recently, W. D. Gao (1996) proved the following theorem: For a cyclic group of prime order, and any element in it, and an arbitrary sequence of elements from , the number of ways of writing as a sum of exactly of the 's is or modulo according as is zero or not. The dual purpose of this note is (i) to give an entirely different type of proof of this theorem; and (ii) to solve a conjecture of J. E. Olson (1976) by answering an analogous question affirmatively for solvable groups.
- W. D. Gao - Two addition theorems on groups of prime order, J. Number Theory, Vol.56 (1996) 211-213.
- J. E. Olson - On a combinatorial problem of Erdös, Ginzburg and Ziv, J. Number Theory, Vol.8 (1976) 52-57. MR 53:2883
Affiliation: School Of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Bombay 400 005 India
Keywords: Chevalley-Warning theorem, combinatorial group theory
Received by editor(s): July 9, 1997
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society