computer divides with 18
Source: Argentina 2000 OMA L3 p4
May 12, 2024
number theory
Problem Statement
A computer program generates a sequence of numbers with the following rule: the first number is written by Camilo; thereafter, the program calculates the integer division of the last number generated by ; thus obtains a quotient and a remainder. The sum of that quotient plus that remainder is the next number generated. For example, if Camilo's number is the computer makes , and generates . The next number generated will be , since and ; etc
Whatever Camilo's initial number is, from some point on, the computer always generates the same number. Determine what is that number that will be repeated indefinitely, if Camilo's initial number is equal to