An interesting determinant occurs in the fifth volume of Muir's History1. It is
where n = ½ (p – 1), and ars is the smallest positive integer such that
rars = s (mod p), (1) p being any odd prime number. It is evident that each element ars is unique and non zero. For p = 5, 7, 11 the determinants are
(2) respectively, and their values are
– 5 , 72, 114.