### Abstract

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

Original language | English (US) |
---|---|

Pages (from-to) | 1341-1346 |

Number of pages | 6 |

Journal | Mathematics of Computation |

Volume | 66 |

Issue number | 219 |

State | Published - Jul 1 1997 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

}

*Mathematics of Computation*, vol. 66, no. 219, pp. 1341-1346.

**On Wendt's determinant.** / Helou, Charles.

Research output: Contribution to journal › Article

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 -