GCD-Closed Sets and the Determinants of GCD Matrices
Scott J. Beslin, Steve Ligh · The Fibonacci Quarterly · 1992
Let S = {xi> x2,..., xn} be a finite ordered set of distinct positive integers. The nxn matrix [S] = (s^-) , where stj = (xi9 Xj), the greatest common divisor of Xi and Xj9 is called the greatest common divisor (GCD) matrix on S (see [2]). In [6], H. J. S. Smith showed that if 5 is a factor-closed set,