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 theorem. Every th root of unity is a primitive th root of unity for exactly one positive divisor of . This implies that This formula represents the factorization of the polynomial into irreducible factors. Applying Möbius inversion to the formula gives where is the Möbius function. So the first few cyclotomic polynomials are If is a prime number, then all the th roots of unity except 1 are primitive th roots, and we have Substituting any positive integer ≥ 2 for , this sum becomes a base repunit. Thus a necessary (but not sufficient) condition for a repunit to be