Ponder This

April 2005

<<March April May>>

Ponder This Challenge:

Puzzle for April 2005

This month's puzzle is sent in by Max Alekseyev. It appeared in a
Russian mathematics olympiad for university students.
It was originally due to Marius Cavache.

We are not asking for submission of answers this month.

Problem:

"b^k" denotes b raised to the k power.

Let a,b be integers greater than 1. Clearly if b=a^k for some positive
integer k, then ((a^n)-1) divides ((b^n)-1) for each positive integer n.
Prove the converse: If ((a^n)-1) divides ((b^n)-1) for each positive
integer n, then b=a^k for some positive integer k.

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

  

Challenge: 04/01/2005 @ 08:30 AM EST
Solution: 05/01/2005 @ 08:30 AM EST
List Updated: 04/01/2005 @ 08:30 AM EST

(No "correct responses" list this month)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.