Mathematics Problem Of the Week

Spring 2005

POW #11: Threes Company!

Let the number A = 33333 ... 333, where the number of times the digit 3 appears is 3³³³.

Is A divisible by 3 with no remainder? Is A divisible by 3² with no remainder? Is A divisible by 3³ with no remainder? What is the highest power of 3 for which A is divisible?

Give reasons for all answers.

Due Friday, April 15^th, at Noon.

Solutions should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/