On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋

Sebastian Tim Holdum; Frederik Ravn Klausen; Peter Michael Reichstein Rasmussen

On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋

Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen

Abstract

We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence [n²/a]. This is done by generalizing a method used by Farhi in his original paper.

Original language	English
Article number	15.6.3
Journal	Journal of Integer Sequences
Volume	18
Issue number	6
ISSN	1530-7638
Publication status	Published - 1 Feb 2015

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title = "On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋",

abstract = "We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence [n2/a]. This is done by generalizing a method used by Farhi in his original paper.",

author = "Holdum, {Sebastian Tim} and Klausen, {Frederik Ravn} and Rasmussen, {Peter Michael Reichstein}",

year = "2015",

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T1 - On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋

AU - Holdum, Sebastian Tim

AU - Klausen, Frederik Ravn

AU - Rasmussen, Peter Michael Reichstein

PY - 2015/2/1

Y1 - 2015/2/1

N2 - We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence [n2/a]. This is done by generalizing a method used by Farhi in his original paper.

AB - We prove some cases of a conjecture by Farhi on the representation of every positive integer as the sum of three terms of the sequence [n2/a]. This is done by generalizing a method used by Farhi in his original paper.

M3 - Journal article

SN - 1530-7638

VL - 18

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 6

M1 - 15.6.3

ER -

On a Conjecture on the Representation of Positive Integers as the Sum of Three Terms of the Sequence ⌊ n2/a ⌋

Abstract

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