Mathematics
Problem Of the Week
Spring
2002
POW #7
Iterated Increasing Integer
Function
Let f(n) be a strictly
increasing function defined on the positive integers which always gives
positive integers as a result (i.e., f:Z+®Z+). If we know that f(f(n))=3n for any positive integer n,
find each of the following (and justify your answers)
(a) f(1)
(b) f(6)
(c) f(100)
(d) f(500)
Due Friday, March 15th at Noon.
(Adapted from a
Macalester College POW)