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Claim. E. Szekeres and G. Szekeres, On a problem of Schütte and Erdős, Math. Gaz. 49 (1965), no. 369, 290--293, DOI 10.2307/3612854 (issued October 1965, the nominal first day of which is this page's date). The paper is not held, and its theorem is stated here as J. W. Moon's review of it gives it (zbMATH, Zbl 0134.43502): by first treating a more general problem, the paper shows that the least order $f(k)$ of a tournament in which every $k$ vertices have a common dominator satisfies $f(k)\ge(k+2)2^{k-1}-1$, and in particular that $f(3)=19$. The review states the bound without a range of $k$; Graham and Spencer (Canad. Math. Bull. 14 (1971), p. 45, display (2)) and Reid, McRae, Hedetniemi and Hedetniemi (Australas. J. Combin. 29 (2004), p. 162, display (2)) also print it without a range, while Jeffries's 2026 preprint (arXiv:2604.08790, Theorem 1.1, item 3) prints it for $k>2$. The range the paper itself states is not known. The bound exceeds $2^{k+1}-1$ for every $k\ge3$, so it refutes Erdős's 1963 guess $f(k)=2^{k+1}-1$. The claim value is proved: the result proves a bound and a value without determining the order of magnitude.

Covers. The lower bound $f(k)\ge(k+2)2^{k-1}-1$ and the value $f(3)=19$; not the order of magnitude, which the problem asks to estimate.

Depends on. Nothing in this wiki.

Acceptance. Refereed: published in The Mathematical Gazette, cited with its venue above. The site credits Szekeres and Szekeres with $f(3)=19$ and $n2^n\ll f(n)$ in commentary on a problem it labels OPEN, which is not acceptance, so reviewed is not listed.

Formalization. The repository jaredwilder/erdos902, linked above at its commit of 18 September 2026, states in Erdos902Szekeres.lean and in its README theorem classical_sandwich the bound $(n+2)2^{n-1}-1\le f(n)$, with $f(3)\ge19$, by a proof the file calls self-contained, making no claim that it is the original argument. This project has not built or audited the repository, so no formalized evidence is listed.