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
Square root of 2 shown to contain no solutions as follows. Since formula_24 is even, formula_29 must be divisible by formula_30, which makes the entire equation congruent to modulo formula_30: The square of any odd number is always formula_33. The square of any even number is always formula_34. Since both formula_18 and formula_19 are odd and formula_24 is even, we have: which is impossible. Therefore, the fifth possibility is also ruled out, leaving the sixth to be the only possible combination to contain solutions, if any. An extension of this lemma is the result that two identical whole-number squares can never be added to