Mathematics Problem Of the Week

Fall 2005

POW #10

Superpowers

For any integer n>0 define a superpower for any number by raising the number to a power of itself n successive times. For example

(a) How many digits are in the value of ?

(b) You can easily check that . Find all values of n, for which is between and . Justify your answer.

Due Friday, November 4^th at Noon

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