constructing sequences by adding simple divisors, common member wanted
Source: Tuymaada Junior 2005 p8
May 12, 2019
number theorynumber theory with sequencesSequence
Problem Statement
The sequence of natural numbers is based on the following rule: each term, starting with the second, is obtained from the previous addition works of all its various simple divisors (for example, after the number should be the number , and after the number , the number ).
Prove that any two sequences constructed in this way have a common member.