Mathematics Problem Of the Week

Spring 2006

POW #11

Integer Induction

(1) Show that has the neat property that is an integer.

(2) Prove that if x is any real number for which is an integer, then is also an integer for any natural number n.

(3) Under what general conditions on real numbers a and b will being an integer imply that must also be an integer for all natural numbers n.

Partial credit may be given for partial answers, but justification is required to win the prize.

Due Friday, April 21^st Noon

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