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Claim. Problem 915 asks whether a graph with $1+n(m-1)$ vertices and $1+n\binom m2$ edges must have two vertices joined by $m$ disjoint paths, and leaves open whether the paths are edge-disjoint or internally vertex-disjoint. W. Mader, Ein Extremalproblem des Zusammenhangs von Graphen, Math. Z. 131 (1973), no. 3, 223--231, answers both readings. Under the edge-disjoint reading the answer is yes for every $m\ge2$: Satz 1 (p. 223) says that a finite graph on $N\ge m$ vertices with more than $\frac m2(N-1)-\frac12\sigma_m(G)$ edges, where $\sigma_m(G)$ sums the deficits $m-1-\deg(x)$ over the vertices of degree below $m-1$, has two vertices joined by $m$ edge-disjoint paths, and its Korollar (p. 226) gives the exact threshold $\ell_m(N)=\lfloor\frac m2(N-1)\rfloor+1$, which at the problem's parameters is $1+n\binom m2$, the conjectured value. Under the vertex-disjoint reading the answer is no for every $m\ge5$: the examples of pp. 228--229 give, for odd $m\ge5$ and even $m\ge6$, graphs on $N$ vertices with $\frac m2(N-1)+j(\frac m2-2)$ edges for odd $m$, or $\frac m2(N-1)+j(m-5)$ for even $m$, where $j$ is the number of cut cliques, and no two vertices joined by $m$ internally disjoint paths, so that no constant $C$ makes $\frac m2N+C$ edges force such a pair; the conjecture would make $k_m(N)=\frac m2N+O(1)$. The site reports the vertex-disjoint examples for $m\ge6$; the printed range includes $m=5$.

The page targets the vertex-disjoint reading, the one the site's curator settled on when he marked the problem solved on 28 October 2025 on the disproof for all $m\ge5$, and the one the formal-conjectures statement for the problem takes; under it the question asks whether the statement holds for every $m\ge2$ and $n\ge1$, and Mader's examples refute it, so the claim value is disproved and the scope is full. The edge-disjoint reading is the variant: Satz 1 and the Korollar prove it for every $m\ge2$ with the exact threshold, which the curator noted as settled, and the formal-conjectures file states it as erdos_915.variants.edge_disjoint. The site's label itself is recorded in the problem page's Status sentence. The vertex-disjoint disproof was first published by Leonard at $m=5$ and extended to every $m\ge5$, with the exact value of $k_5(n)$, by Sørensen and Thomassen; Mader's paper is the one result that answers both readings.

Acceptance. Refereed: Mathematische Zeitschrift (volume 131, issue 3, pp. 223--231, issued September 1973 by its Crossref record, accessed 2026-10-07; the day is the issue's nominal first day, used for this page's date). Reviewed: the site's curator (T. F. Bloom), independent of the author, credits the paper with both results in the problem's commentary and labeled the problem solved on 28 October 2025, after a thread reading of the German original (27 October 2025) confirmed the printed definition of $\sigma_m(G)$; Sørensen and Thomassen report the vertex-disjoint examples in the introduction of their 1974 paper (p. 143). The source has a library source card. Read depth: Satz 1, the Korollar and the examples; the proofs are not checked, and the existence of the regular graphs with cut cliques that the examples start from is asserted without an argument in print. The acceptance rests on the publication and the site's acceptance; nothing is independently reviewed by this project.