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Claim. Van der Waerden's conjecture: every doubly stochastic $n\times n$ matrix $X$ satisfies $\operatorname{per}(X)\ge n!/n^n$. The permanent is the sum over the $n!$ permutations $\sigma$ of the diagonal products $\prod_i x_{i\sigma(i)}$, so their average is at least $n^{-n}$ and some $\sigma$ attains $\prod_i x_{i\sigma(i)}\ge n^{-n}$, which is the statement of Problem 499. The site's commentary credits G. P. Egorychev [Eg81] with a proof of the conjecture, independent of Falikman's (claim page); the paper proves the conjecture as stated above, and the publication records list the result first as the preprint The solution of the van der Waerden problem for permanents (Akad. Nauk SSSR Sibirsk. Otdel., Inst. Fiz., Krasnoyarsk, preprint IFSO-13 M, 1980), the first posting, which carries no month, so the page carries the first day of that year.

Acceptance. Refereed: the site's citation is Dokl. Akad. Nauk SSSR 258 (1981), 1041–1044 (English translation Soviet Math. Dokl. 23 (1981), 619–622); the proof also appeared as The solution of van der Waerden's problem for permanents, Adv. Math. 42 (1981), no. 3, 299–305, and as Proof of the van der Waerden conjecture for permanents, Sibirsk. Mat. Zh. 22 (1981), no. 6, 65–71 (English translation Siberian Math. J. 22 (1981), no. 6, 854–859). The site's curator records the proofs of van der Waerden's conjecture but credits the problem's own statement to Marcus and Minc, whose earlier direct proof is the credited claim; this page therefore lists no reviewed evidence. The deduction from the permanent bound to the diagonal bound is the one-line averaging above.