2010 AIME I Problems/Problem 5
Contents
[hide]Problem
Positive integers , , , and satisfy , , and . Find the number of possible values of .
Solution
Solution 1
Using the difference of squares, , where equality must hold so and . Then we see is maximal and is minimal, so the answer is .
Solution 2
Since must be greater than , it follows that the only possible value for is (otherwise the quantity would be greater than ). Therefore the only possible ordered pairs for are , , ... , , so has possible values.
See Also
2010 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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