# 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 language English (US) 1341-1346 6 Mathematics of Computation 66 219 Published - 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.
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Helou, C 1997, 'On Wendt's determinant', Mathematics of Computation, vol. 66, no. 219, pp. 1341-1346.
In: Mathematics of Computation, Vol. 66, No. 219, 01.07.1997, p. 1341-1346.

Research output: Contribution to journalArticle

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