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2018 PUMaC Algebra A3

Source:

November 25, 2018

PuMACalgebra

Problem Statement

Let

x_0, x_1, \ldots

be a sequence of real numbers such that

x_n = \frac{1 + x_{n -1}}{x_{n - 2}}

for

n \geq 2

. Find the number of ordered pairs of positive integers

(x_0, x_1)

such that the sequence gives

x_{2018} = \frac{1}{1000}