MathDB
A series with special terms and complete residue system

Source: Miklós Schweitzer 2015 P4

November 10, 2015
number theorynumber theory proposedlimitslimitalgebra and number theoryprime numbers

Problem Statement

Let ana_n be a series of positive integers with a1=1a_1=1 and for any arbitrary prime number pp, the set {a1,a2,⋯ ,ap}\{a_1,a_2,\cdots,a_p\} is a complete remainder system modulo pp. Prove that lim⁡n→∞ann=1\lim_{n\rightarrow \infty} \cfrac{a_n}{n}=1.
Back to ProblemsView on AoPS