MathDB

A3

Part of 1979 Putnam

Problems(1)

Putnam 1979 A3

Source:

4/8/2022
Let x1,x2,x3,…x_1,x_2,x_3, \dots be a sequence of nonzero real numbers satisfying xn=xn−2xn−12xn−2−xn−1 for n=3,4,5,… .x_n=\frac{x_{n-2}x_{n-1}}{2x_{n-2}-x_{n-1}} \text{ for } n=3,4,5, \dots. Establish necessary and sufficient conditions on x1x_1 and x2x_2 for xnx_n to be an integer for infinitely many values of n.n.
college contests