On Wendt's determinant

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Wendt's determinant of order m is the circulant determinant Wm whose (i, j)-th entry is the binomial coefficient (|i-j|m), for 1 ≤ i, j ≤ m. We give a formula for Wm, when m, is even not divisible by 6, in terms of the discriminant of a polynomial Tm+i, with rational coefficients, associated to (X + 1)m+1 - Xm+1 - 1. In particular, when m = p - 1 where p is a prime ≡ - 1 (mod 6), this yields a factorization of Wp-1 involving a Fermat quotient, a power of p and the 6-th power of an integer.

Original languageEnglish (US)
Pages (from-to)1341-1346
Number of pages6
JournalMathematics of Computation
Volume66
Issue number219
StatePublished - Jul 1 1997

Fingerprint

Factorization
Determinant
Fermat quotient
Polynomials
Binomial coefficient
Divisible
Discriminant
Polynomial
Integer
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Helou, Charles. / On Wendt's determinant. In: Mathematics of Computation. 1997 ; Vol. 66, No. 219. pp. 1341-1346.
@article{0a45f3e0079b4520b82cdd2698c7a224,
title = "On Wendt's determinant",
abstract = "Wendt's determinant of order m is the circulant determinant Wm whose (i, j)-th entry is the binomial coefficient (|i-j|m), for 1 ≤ i, j ≤ m. We give a formula for Wm, when m, is even not divisible by 6, in terms of the discriminant of a polynomial Tm+i, with rational coefficients, associated to (X + 1)m+1 - Xm+1 - 1. In particular, when m = p - 1 where p is a prime ≡ - 1 (mod 6), this yields a factorization of Wp-1 involving a Fermat quotient, a power of p and the 6-th power of an integer.",
author = "Charles Helou",
year = "1997",
month = "7",
day = "1",
language = "English (US)",
volume = "66",
pages = "1341--1346",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "219",

}

Helou, C 1997, 'On Wendt's determinant', Mathematics of Computation, vol. 66, no. 219, pp. 1341-1346.

On Wendt's determinant. / Helou, Charles.

In: Mathematics of Computation, Vol. 66, No. 219, 01.07.1997, p. 1341-1346.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On Wendt's determinant

AU - Helou, Charles

PY - 1997/7/1

Y1 - 1997/7/1

N2 - Wendt's determinant of order m is the circulant determinant Wm whose (i, j)-th entry is the binomial coefficient (|i-j|m), for 1 ≤ i, j ≤ m. We give a formula for Wm, when m, is even not divisible by 6, in terms of the discriminant of a polynomial Tm+i, with rational coefficients, associated to (X + 1)m+1 - Xm+1 - 1. In particular, when m = p - 1 where p is a prime ≡ - 1 (mod 6), this yields a factorization of Wp-1 involving a Fermat quotient, a power of p and the 6-th power of an integer.

AB - Wendt's determinant of order m is the circulant determinant Wm whose (i, j)-th entry is the binomial coefficient (|i-j|m), for 1 ≤ i, j ≤ m. We give a formula for Wm, when m, is even not divisible by 6, in terms of the discriminant of a polynomial Tm+i, with rational coefficients, associated to (X + 1)m+1 - Xm+1 - 1. In particular, when m = p - 1 where p is a prime ≡ - 1 (mod 6), this yields a factorization of Wp-1 involving a Fermat quotient, a power of p and the 6-th power of an integer.

UR - http://www.scopus.com/inward/record.url?scp=0031520144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031520144&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031520144

VL - 66

SP - 1341

EP - 1346

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 219

ER -