Reducing numbers
Source: Mexican Mathematical Olympiad 2014 Problem 2
November 11, 2014
number theory proposednumber theory
Problem Statement
A positive integer is said to reduce to a positive integer if when dividing by its units digits the result is . For example, 2015 reduces to .
Find all the positive integers that become 1 after some amount of reductions. For example, 12 is one such number because 12 reduces to 6 and 6 reduces to 1.