Integer Sets Containing No Solution to $$x + y = 3z$$

Fan R. K. Chung () and John L. Goldwasser ()
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Fan R. K. Chung: University of California, Department of Mathematics
John L. Goldwasser: West Virginia University, Department of Mathematics

A chapter in The Mathematics of Paul Erdős I, 2013, pp 147-157 from Springer

Abstract: Summary We prove that a maximum subset of $$\{1,2,\ldots,n\}$$ containing no solutions to $$x + y = 3z$$ has $$\lceil \frac{n} {2} \rceil$$ elements if n≠4, thus settling a conjecture of Erdős. For n≥23 the set of all odd integers less than or equal to n is the unique maximum such subset.

Keywords: Large Integer; Unique Maximum; Maximum Subset; Continuous Analog; Distinct Integer (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_11

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DOI: 10.1007/978-1-4614-7258-2_11

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