Department of Mathematics and Statistics
Problem of the Month
Problem 4, April 2013
Determine all the differentiable real functions f from R to R whose composition with themselves, fof, is the original function f.
Problem suggested by Professor Sam Nadler from The University of Toledo
Please submit your solution for this month problem no later than 15 of the next month. Try to keep
your solution to less than two pages. My office is in MSC 426 and my email address is
email@example.com You may also put your solution in my mailbox (Mihai Staic).
If you want to propose a problem please contact me by email or in person.
Each student that submits a solution will will receive points and at the end of the academic year
a few certificates will be awarded by the Mathematics and Statistics Department.
Problem 1, August 2012
A page (two sides) is torn from a paperback novel. The sum of the remaining page numbers
is 15000. Which page was torn out? (Rasor-Bareis Exam 1996) Solution
Correct solutions were submitted by: Mike Hughes, Devin Bender, Suzanne Hirsel. There were
other students that submitted partially correct solution.
Problem 2, September 2012
Consider a bounded solid S that has the following property: Whenever we intersect S with a
plane the intersection is either the empty set or a point or a disk. Show that S must be a
sphere (a ball).
Problem 3, October 2012
Find all functions f from R to R such that f(x+y)=f(x)+f(y) and f(xy)=f(x)f(y) for all x and
y in R.