Limit help limit of fractional part function power

foxofdesert
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It's also true if you substitute sqrt(5)+sqrt(7) or sqrt(3)+sqrt(5) or sqrt(13)+sqrt(11). I tried sqrt(3)+sqrt(11) and it doesn't seem to be true for that guy, so it's hard to tell but it seems like there should be a general proof that doesn't rely on adding up multiples of sqrt(6) and watching stuff cancel out. I can't fathom what it is though
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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