MathDB
Show identity involving logarithmic and power functions

Source: Indian Postal Coaching 2012 Set 1 #3

September 19, 2013
functionfloor functionlogarithmsalgebra unsolvedalgebraInteger Part

Problem Statement

Given an integer n≥2n\ge 2, prove that ⌊n⌋+⌊n3⌋+⋯+⌊nn⌋=⌊log⁡2n⌋+⌊log⁡3n⌋+⋯+⌊log⁡nn⌋\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)
Back to ProblemsView on AoPS