This number is the larger of the two perfect powers mentioned in the Catalan Conjecture.
This number is the larger of the two perfect powers mentioned in the Catalan Conjecture. According to the k equals three case of Waring's Problem, every integer can be written as a sum of at most this many cubes. Though it's not three, the difference between a number and a rearrangement of its digits will always be divisible by this number, and a given number is divisible by this number if repeatedly summing its digits eventually yields this number. This is the smallest number with (*) three odd factors, a consequence of it being the square of an odd prime number. For ten points, identify this number equal to three squared.
This number is the larger of the two perfect powers mentioned in the Catalan Conjecture.
{nine}