Problem #PRU-97790

Problems Methods Algebraic methods Counting in two ways Algebra Exponential functions and logarithms Exponential functions and logarithms (other) Calculus Real numbers Integer and fractional parts. Archimedean property

16–18 4.0

Problem

Prove that for every natural number $n > 1$ the equality: $⌊ n^{1 / 2} ⌋ + ⌊ n^{1 / 3} ⌋ + \dots + ⌊ n^{1 / n} ⌋ = ⌊ \log_{2} n ⌋ + ⌊ \log_{3} n ⌋ + \dots + ⌊ \log_{n} n ⌋$ is satisfied.

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