Limit of fractional part function to a power

[foxofdesert]

solved.

 

[Office_Shredder]

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