ON A PROBLEM OF CARLITZ-Reference-Cited by-同舟云学术

ON A PROBLEM OF CARLITZ

Published:2005-06 Issue:02 Volume:01 Page:293-307
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BAOULINA IOULIA¹

Affiliation:

1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India

Abstract

Let Nq be the number of solutions to the equation [Formula: see text] over the finite field [Formula: see text]. Carlitz found formulas for Nq when n = 3 or 4. In an earlier paper, we found formulas for Nq when d = gcd (n - 2, q - 1) = 1 or 2 or 3 or 4; and when there exists an l such that pl ≡ -1 (mod d). In another paper the cases d = 7 or 14, p ≡ 2 or 4 (mod 7) were considered. In this paper, we find formulas for Nq when d = 8. We also simplify formulas for Nq when d = 4, p ≡ 1 (mod 4).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042105000194

Reference6 articles.

1. Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer

2. Complete solution of the cyclotomic problem in $F_q$ for any prime modulus $l, q = p^α, p ≡ 1 (mod l)$

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