Problem of the Week: Powerful Numbers
Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
THE RULES:
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Send solutions to bkennedy@gettysburg.edu. This problem was posted on Saturday, March 26 and solutions are due on Friday, April 1 by 5:00 p.m.
THE PROBLEM:
Let m be an integer (that is, a whole number — perhaps positive, perhaps negative, perhaps zero). Let us say that m is a Sum-Power-Average (SPA) number if there are positive whole numbers k and j such that
QUESTION:
Find all the SPA numbers. In your solution, explain how you know your list is complete.
