For any positive integer x define g(x) as greatest odd divisor of x, and
f(x) \equal{} \begin{cases} \frac {x}{2} \plus{} \frac {x}{g(x)} & \text{if \ $$x$$ is even}, \\
2^{\frac {x \plus{} 1}{2}} & \text{if \ $$x$$ is odd}. \end{cases}
Construct the sequence x_1 \equal{} 1, x_{n \plus{} 1} \equal{} f(x_n). Show that the number 1992 appears in this sequence, determine the least n such that x_n \equal{} 1992, and determine whether n is unique. inductionalgebrarecurrence relationSequenceIMO ShortlistIMO Longlist