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.
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Chung, F.R.K., Goldwasser, J.L. (2013). Integer Sets Containing No Solution to \(x + y = 3z\) . In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_11
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DOI: https://doi.org/10.1007/978-1-4614-7258-2_11
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