Given an integer $n\ge 2$, prove that \[\lfloor \sqrt n \rfloor + \lfloor \sqrt[3]n\rfloor + \cdots +\lfloor \sqrt[n]n\rfloor = \lfloor \log_2n\rfloor + \lfloor \log_3n\rfloor + \cdots +\lfloor \log_nn\rfloor\].
HIDE: Edit Thanks to shivangjindal for pointing out the mistake (and sorry for the late edit)Problem
Source: Indian Postal Coaching 2012 Set 1 #3
Tags: function, floor function, logarithms, algebra unsolved, algebra, Integer Part