Problem Contest -
Problem of the Week – November 16, 2004
A Problem About Powers of Positive Integers: Let f(x) = xn where n is a fixed positive integer and x runs through all positive integers 1, 2, 3, … . Let yn be the infinite decimal
0.f(1)f(2)f(3)… where the numbers f(1), f(2), f(3) … are placed end-to-end.
Example: y2 = .14916253649… .
Is yn ever a rational number for some value of n?
Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, November 30. Or leave them in the Warner mailroom.
Note: Join us at the weekly seminars, usually on Tuesday at 3:00 for refreshments.