On Wendt's determinant

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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
DOIs
StatePublished - Jul 1997

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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