Problem of the Week 1141Capturing Five IntegersFor 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.
