Sequence and product of digits
Source: Argentina TST Iberoamerican 2009 Problem 5
August 25, 2009
number theory unsolvednumber theory
Problem Statement
Let and be positive integers. Let be the sequence defined by
a_1 \equal{} a and
a_{n \plus{} 1} \equal{} a_n \plus{} k\pi(a_n)
where
is the product of the digits of (written in base ten)
Prove that we can choose and such that the infinite sequence contains exactly distinct terms