3

Part of 1986 Federal Competition For Advanced Students, P2

Problems(1)

infinitely many natural numbers

Source: Austria 1986

Find all possible values of

x_0

x_1

such that the sequence defined by: x_{n\plus{}1}\equal{}\frac{x_{n\minus{}1} x_n}{3x_{n\minus{}1}\minus{}2x_n} for

n \ge 1

contains infinitely many natural numbers.

algebrapolynomiallimitalgebra proposed