Mathematics Problem Of the Week

Fall 2007

POW #8

Base-free Mathematics:

More Fun with 1's

It is a well-known fact that 11²=121. It is less appreciated that this result holds for all positive integer bases (except binary).

For example, in base 3, 11 represents 4 and 121 represents 1*9+2*3+1=16. Similarly in base 5, 11 represents 6 and 121 represents 1*25+2*5+1=36.

Explore analogous results for 111², 1111² and so on, and give a general description and justification/explanation of the results.

Due Friday, November 2^nd at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.