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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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On solution-free sets for simultaneous polynomial equations
by
Matthew Smith
University of Georgia

We use methods from additive combinatorics to establish a bound for the upper density of a set of integers containing no solutions to the pair of equations ∑i=13(xi2-yi2)=P2(n), ∑i=13(xi-yi)=P1(n), where P2 and P1 are polynomials with integer coefficients and zero constant term and n is any integer.

Date received: June 11, 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-81.