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Sequence with all Integers

Source: 1988 IrMO Paper 1 Problem 8

September 28, 2017
algebra

Problem Statement

Let x1,x2,x3,…x_1,x_2,x_3,\dots be sequence of nonzero real numbers satisfying x_n=\frac{x_{n-2}x_{n-1}}{2x_{n-2}-x_{n-1}},     n=3,4,5,\dots Establish necessary and sufficient conditions on x1,x2x_1,x_2 for xnx_n to be an integer for infinitely many values of nn.
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