UKMT Senior Challenge-V
What is the largest three-digit integer that can be written in the form
where
is an integer?
This problem is not original.This problem is part of this set .
The answer is 992.
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1 solution
the form n+√n can be written by taking √n as a common factor, it becomes √n (√n+1) .. which means that now we are looking for 2 consecutive numbers that their product is the maximum three digit number we can get .. by trying we find that the largest three digit number can be obtained by 31 32 .. now all what we need to do is to raise 31 to the second power so it becomes 961 and this is our n