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Root sum equals integer (Posted on 2015-03-10) Difficulty: 3 of 5
Find all integers n for which √(25/2 + √(625/4 –n)) + √(25/2 - √(625/4 –n)) is an integer.

No Solution Yet Submitted by K Sengupta    
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re: solution & playing around | Comment 3 of 7 |
(In reply to solution & playing around by Jer)

Although the individual terms of f(n) can be complex, they are complex conjugates outside the domain of either one of them individually, so f(n) can be real beyond 625/4. For example, for n=784, 


f(784) = 4.5+2.783882181415010961*i  +  4.5-2.783882181415010961*i 

and the sum of the two terms is 9.

The coefficient of each i (positive and negative) in this case is sqrt(7.75).

  Posted by Charlie on 2015-03-10 14:40:30
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