400 (number) third perfect number, a number whose divisors add up to the actual number (1+2+4+8+16+31+62+124+248=496). 497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107) 498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number A prime number, Chen prime 400 (number) 400 (four hundred) is the natural number following 399 and preceding 401. 400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111). A circle is divided into
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