On the solutions of the equation 𝑥^{𝑚}+𝑦^{𝑚}-𝑧^{𝑚}=1 in a finite field-Reference-Cited by-同舟云学术

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On the solutions of the equation 𝑥^{𝑚}+𝑦^{𝑚}-𝑧^{𝑚}=1 in a finite field

Published:1995 Issue:5 Volume:123 Page:1331-1339
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Ke Wen Fong,Kiechle Hubert

Abstract

An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only on m and the characteristic of the field, holds.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1995-123-05/S0002-9939-1995-1234628-4/S0002-9939-1995-1234628-4.pdf

Reference19 articles.

1. Circular block designs from planar near-rings;Clay, James R.,1988

2. Oxford Science Publications;Clay, James R.,1992

3. Linear codes from planar nearrings and Möbius planes;Clay, James R.;Algebras Groups Geom.,1993

4. Cyclotomy, Higher Congruences, and Waring’s Problem;Dickson, L. E.;Amer. J. Math.,1935

5. \bysame, Congruences involving only e-th powers, Acta Arith. 1 (1936), 161-167.

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