MathDB
a_n = c x \phi (a_{n-1}) , is bounded

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 1 E+1

November 29, 2022
Euler s Phi Functionphi functionnumber theorySequence

Problem Statement

Let c≥2c \ge 2 be a fixed integer. Let a1=ca_1 = c and for all n≥2n \ge 2 let an=c⋅ϕ(an−1)a_n = c \cdot \phi (a_{n-1}). What are the numbers cc for which sequence (an)(a_n) will be bounded?
ϕ\phi denotes Euler’s Phi Function, meaning that ϕ(n)\phi (n) gives the number of integers within the set {1,2,...,n}\{1, 2, . . . , n\} that are relative primes to nn. We call a sequence (xn)(x_n) bounded if there exist a constant DD such that ∣xn∣<D|x_n| < D for all positive integers nn.
Back to ProblemsView on AoPS