2008 AIME I Problems/Problem 7
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 (which is when ), 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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
Video Solution: https://www.youtube.com/watch?v=6eBLXnzK0n4 The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.