MathDB
bounded and periodic sequence

Source:

February 25, 2006
pigeonhole principleLaTeXnumber theory proposednumber theory

Problem Statement

Let cc be fixed natural number. Sequence (an)(a_n) is defined by: a1=1a_1=1, an+1=d(an)+ca_{n+1}=d(a_n)+c for n=1,2,...n=1,2,.... where d(m)d(m) is number of divisors of mm. Prove that there exist kk natural such that sequence ak,ak+1,...a_k,a_{k+1},... is periodic.
Back to ProblemsView on AoPS