Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T13:48:59.413Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous Pairs of Linear and Quadratic Equations In a Galois Field

Published online by Cambridge University Press:  20 November 2018

Eckford Cohen
Eckford Cohen*
Affiliation:
University of Tennessee
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F denote the Galois field GF(pr) with pr elements, where p is an odd prime and r is a positive integer. Suppose further that m and n are arbitrary elements of F and that αi, βi pt (i = 1, …, s) are nonzero elements of F. The purpose of this paper is to evaluate the function Ns(m, n), defined, for an arbitrary positive integer s, to be the number of simultaneous solutions in F of the equations

1.1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 74 - 78
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Carlitz, Leonard, Weighted quadratic partitions over a finite field, Can. J. Math., 5 (1953), 317–323.Google Scholar
2. Dickson, L. E., Linear Groups (Leipzig, 1901).Google Scholar
3. O'Connor, R. E., Quadratic and linear congruence, Bull. Amer. Math. Soc, 45 (1939), 792–798.Google Scholar
4. O'Connor, R. E. and Pall, Gordon, The quaternion congruence (mod g), Amer. J. Math., 61 (1939), 487–508.Google Scholar
5. Whiteman, A. L., Finite Fourier series and equations in finite fields, Trans. Amer. Math. Soc, 54 (1953), 78–98.Google Scholar