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Claim. Michael Beeson, No triangle can be cut into seven congruent triangles, arXiv:1811.09723 (version 1 posted 23 November 2018, version 5 of 17 June 2019), proves the theorem of its title and the same for eleven: no triangle can be cut into $7$ or into $11$ congruent triangles. By its abstract, earlier work reduces the question to a number of cases, and the paper settles the cases not already solved; its later revision replaced the treatment of isosceles triangles by a citation to Beeson's paper on isosceles tilings (arXiv:1206.1974). The site's remarks on Problem 634 credit Beeson with the exclusion of $7$ and $11$ and link Beeson's talk slides; this paper is the written source. Beeson's 2026 preprint on the prime counts (claim page) describes this paper's method as direct and short but unable to reach $19$.

Covers. The values $7$ and $11$ do not occur as the number of congruent triangles into which some triangle can be cut. Nothing is claimed about other values of $n$.

Depends on. No page of this wiki.

Standing. Claimed. The paper has no journal record; the site labels the problem OPEN, so the curator's credit is commentary, not acceptance. The primes $7$ and $11$ are also excluded by the three 2026 prime manuscripts and, $7$ unconditionally and $11$ by certified exhaustive search, by Bonfioli's manuscript (claim page), which lists $11$ among the values it says the published theorems do not settle, because the exclusions in Beeson's paper on the case $3\alpha+2\beta=\pi$ (arXiv:1206.2229) rest on a divisibility it refutes; this page records that dispute without resolving whether it reaches the argument of this paper.