Arithmetical properties of wendtʹs determinant Original Research Article

Wendtʹs determinant of order n is the circulant determinant Wn whose (i,j)-th entry is the binomial coefficient image, for 1less-than-or-equals, slanti,jless-than-or-equals, slantn, 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 image and image. If q is another prime, distinct from p, and h any positive integer, then image. Furthermore, if p is odd, then image. In particular, if pgreater-or-equal, slanted5, then image. Also, if m and n are relatively prime positive integers, then WmWn divides Wmn.