Remarks on certain sums involving floor function

Wachiraya Palatsang^a, Prapanpong Pongsriiam^b,*, Tammatada Khemaratchatakumthorn^b, Kittipong Subwattanachai^b, Naruesorn Khuntijit^a, Narongkorn Kitnak^a

ABSTRACT: For each a = 1,2, 3,. .. ,7, there exists an integer b depending on a such that nXk=1 ›akž = ›(2n8+ab)2ž for all n 2 N. In this article, we give some remarks on this identity. In particular, we show that the range of a cannot be extended and the value of b is unique.

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^a	Faculty of Education, Silpakorn University, Nakhon Pathom 73000 Thailand
^b	Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000 Thailand

* Corresponding author, E-mail: prapanpong@gmail.com, pongsriiam_p@silpakorn.edu

Received 11 Feb 2021, Accepted 9 May 2021

Remarks on certain sums involving floor function

Wachiraya Palatsanga, Prapanpong Pongsriiamb,*, Tammatada Khemaratchatakumthornb, Kittipong Subwattanachaib, Naruesorn Khuntijita, Narongkorn Kitnaka

Wachiraya Palatsang^a, Prapanpong Pongsriiam^b,*, Tammatada Khemaratchatakumthorn^b, Kittipong Subwattanachai^b, Naruesorn Khuntijit^a, Narongkorn Kitnak^a