Mock AIME 2 2006-2007 Problems/Problem 3
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Problem
Let be the sum of all positive integers such that is a perfect square. Find the remainder when is divided by
Solution
If , we can complete the square on the left-hand side to get so . Subtracting and factoring the left-hand side, we get . , which can be split into two factors in 3 ways, . This gives us three pairs of equations to solve for :
and give and .
and give and .
and give and .
Finally, , so the answer is .
See Also
Mock AIME 2 2006-2007 (Problems, Source) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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