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