MathDB
2013-2014 Fall OMO #8

Source:

October 30, 2013
Online Math Open

Problem Statement

Suppose that x1<x2<⋯<xnx_1 < x_2 < \dots < x_n is a sequence of positive integers such that xkx_k divides xk+2x_{k+2} for each k=1,2,…,n−2k = 1, 2, \dots, n-2. Given that xn=1000x_n = 1000, what is the largest possible value of nn?
Proposed by Evan Chen
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