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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Simultaneous diagonal equations of odd degrees
by
Michael P. Knapp
Loyola College

In this talk, we will consider a system of two diagonal equations
a1x1k + ...+ asxsk = 0
b1x1n + ...+ bsxsn = 0
over a p-adic field Qp, where the degrees k and n are odd and k ≥ n. We will show that if (k, n) ≠ (5, 3) and the number of variables is at least k2 + n2 + 1, then this system must have a nontrivial solution in p-adic integers.

Date received: June 12, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-84.