Difference between revisions of "2006 SMT/General Problems/Problem 10"
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Revision as of 17:58, 13 January 2020
Solution
First of all, lets note that the sum of all positive integers from 
to 
inclusive is 
. The sum of all numbers from to 
is then:
![\[\frac{2006(2007)}{2} = (1003)(2007)\]](http://latex.artofproblemsolving.com/5/a/9/5a99ba0ce38d9a15c0f7161dfc41a747c1dda9bb.png)
Finding the prime factorization of the product, we see that:
![\[(1003)(2007)=17 \cdot 59 \cdot 3^2 \cdot 223\]](http://latex.artofproblemsolving.com/9/f/0/9f06a9d84c6c14f14d9df2d330e499bec0ef8873.png)
Taking the square root, the answer is:
![\[\sqrt{(1003)(2007)}=\sqrt{17 \cdot 59 \cdot 3^2 \cdot 223} = 3\sqrt{17 \cdot 59 \cdot 223} = \boxed{3\sqrt{223669}}\]](http://latex.artofproblemsolving.com/5/b/d/5bdc227581e1df87a9d52dc1b5cff8bd63fd1dfe.png)
