Problem of the Fortnight #14

 

A Real Powerful Puzzle

 

Let be real numbers.

 

A)    Prove that if is an integer then is an integer for every natural number .

B)     Determine conditions on andsuch that if is an integer then is an integer for every natural number.  Provide rigorous arguments.

 

Solutions are due by 4pm on Friday, April 28th in Goodrich 108.