MathDB
How many integers at least belong to this sequence?

Source: China Team Selection Test 2003, Day 2, Problem 3

October 13, 2005
inductionmodular arithmeticalgebrabinomial theoremalgebra unsolved

Problem Statement

Let (xn) \left(x_{n}\right) be a real sequence satisfying x0=0 x_{0}=0, x2=23x1 x_{2}=\sqrt[3]{2}x_{1}, and xn+1=143xn+43xn−1+12xn−2 x_{n+1}=\frac{1}{\sqrt[3]{4}}x_{n}+\sqrt[3]{4}x_{n-1}+\frac{1}{2}x_{n-2} for every integer n≥2 n\geq 2, and such that x3 x_{3} is a positive integer. Find the minimal number of integers belonging to this sequence.
Back to ProblemsView on AoPS