Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.8

Approximating Sums of Consecutive Integral Roots

Pongpol Ruankong and Kantaphon Kuhapatanakul
Department of Mathematics
Faculty of Science
Kasetsart University
Bangkok 10900


We present an alternative proof of Saltzman and Yuan’s result on the sums of consecutive integral roots. We use the AM-GM-HM inequality to prove the main result. Moreover, the lower bound for which the result holds is greatly improved.

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Received April 30 2019; revised version received September 2 2019. Published in Journal of Integer Sequences, September 25 2019.

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