2008 AIME I Problems/Problem 7
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Problem
Let be the set of all integers such that . For example, is the set . How many of the sets do not contain a perfect square?
Solution
The difference between consecutive squares is , which means that all squares above are more than apart.
Then the first sets () each have at least one perfect square. Also, since , there are other sets after that have a perfect square.
There are sets without a perfect square.
See also
2008 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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