Digital root number is the number mod 11 (Ɛ), for example, 1972 is 1 + 9 + 7 + 2 = 19 = 17 which is 1 + 7 = 8, while in decimal the root of the same number (3110) is 5; and in base 16 a digital root of a number is the number mod 15 (0xF), for example, 0x7DF is 7 + 13 + 15 = 35 = 0x23 which is 2 + 3 = 5, while in decimal the root of the same number (2015) is 8. Digital roots form an important mechanic in the visual novel adventure
Root of unity modulo n a primitive formula_25-th root of unity because there is the smaller exponent formula_72. That is, by exponentiating "x" one can obtain formula_84 different primitive "k"-th roots of unity, but these may not be all such roots. However, finding all of them is not so easy. You may want to know, in what integer residue class rings you have a primitive "k"-th root of unity. You need it for instance if you want to compute a Discrete Fourier Transform (more precisely a Number theoretic transform) of a formula_25-dimensional integer vector. In order to perform the inverse transform, you also need to