Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496435 | Journal of Number Theory | 2005 | 13 Pages |
Abstract
Wendt's determinant of order n is the circulant determinant Wn whose (i,j)-th entry is the binomial coefficient n|i-j|, for 1⩽i,j⩽n, where n is a positive integer. We establish some congruence relations satisfied by these rational integers. Thus, if p is a prime number and k a positive integer, then Wpkâ¡1(modpk) and Wnpkâ¡Wn(modp). If q is another prime, distinct from p, and h any positive integer, then Wphqkâ¡WphWqk(modpq). Furthermore, if p is odd, then Wpâ¡1+p2p-1p-1-1(modp5). In particular, if p⩾5, then Wpâ¡1(modp4). Also, if m and n are relatively prime positive integers, then WmWn divides Wmn.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Charles Helou, Guy Terjanian,