Persistence of a number assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest
Polydivisible number Polydivisible numbers represent a generalization of the following well-known problem in recreational mathematics : The solution to the problem is a nine-digit polydivisible number with the additional condition that it contains the digits 1 to 9 exactly once each. There are 2,492 nine-digit polydivisible numbers, but the only one that satisfies the additional condition is Other problems involving polydivisible numbers include: Polydivisible number In mathematics a polydivisible number (or magic number) is a number with digits "abcde..." that has the following properties : For example, 345654 is a six-digit polydivisible number, but 123456 is not, because 1234 is not a