Problem:
The increasing sequence consists of all positive integers that are neither the square nor the cube of a positive integer. Find the term of this sequence.
Solution:
Between and , there are perfect squares and perfect cubes. Among these integers there are of them ( and ) that are counted twice. Thus there are integers between and that are not in the sequence. To get the number, we must append integers to the list of non-squares and non-cubes. Since we cannot use , the last number will be .
The problems on this page are the property of the MAA's American Mathematics Competitions