1990 AIME Problems/Problem 1
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Problem
The increasing sequence 
consists of all positive integers that are neither the square nor the cube of a positive integer. Find the 500th term of this sequence.
Solution
Because there aren't that many perfect squares or cubes, let's look for the smallest perfect square greater than 
. This happens to be 
. Notice that there are 
squares and 
cubes less than or equal to 
, but 
and 
are both squares and cubes. Thus, there are 
numbers in our sequence less than . Magically, we want the 
term, so our answer is the smallest non-square and non-cube less than , which is 
.
See also
| 1990 AIME (Problems • Resources) | ||
| Preceded by First Question | Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
