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Problem of the Week 1141
Capturing Five Integers
For which positive real numbers x are there exactly 5 integers n such that the following statement is true?
x < n < x²
Source: A variation by me of a problem by Bill Sands in the Feb. issue of Crux Mathematicorum.
Extra credit: Given N, describe the set S(N) of real numbers x such that there are exactly N integers in the open interval determined by x and x².
© Copyright 2011 Stan Wagon. Reproduced with permission.