The site's wording is Erdős's. In [Er64b], p. 62, after the theorem of Hecke and Ostrowski (display (24)) that $N_n(u,v)=n(v-u)+O(1)$ when both $u$ and $v$ are of the form $(k\alpha)$, Erdős writes: "Szüsz and I conjectured the converse of this theorem, i.e. if (24) holds then $u=(k_1\alpha)$, $v=(k_2\alpha)$, unfortunately we had not been able to make any progress with this conjecture" (the conjecture card). Boris Alexeev's Lean theorem not_erdos_998 (formal authors Codex and GPT-5.6 Sol) refutes that endpoint converse for $\alpha=\sqrt2/10$, $u=1/4$. The site labels the problem PROVED and its commentary says "This is true, and was proved by Kesten [Ke66]." The theorem credited, Theorem 4 of Kesten's paper (Acta Arith. 12 (1966), p. 193), is the length criterion: for fixed $\xi$ and $0\le a<b\le1$ with $b-a<1$, the discrepancy of $[a,b)$ is bounded in $M$ if and only if $b-a=\{j\xi\}$ for some integer $j$. Kesten writes that this "confirms a recent conjecture of Erdős and Szüsz [2]" and, in Section 4, that "except for a slight modification this was conjectured by Erdős and Szüsz ([2], p. 61)"; the modification is the passage from the two endpoints to the length, made by the prover and adopted by the site's label and attribution. The page follows that reading. The corrected Statement replaces the conclusion "$u=\{\alpha k\}$ and $v=\{\alpha\ell\}$ for some integers $k$ and $\ell$" by "$v-u=\{\alpha j\}$ for some integer $j$" and adds Kesten's range $0\le u<v\le1$, $v-u<1$, which excludes only the full interval $[0,1)$, whose discrepancy is identically $0$ and whose length $1$ is not a fractional part; nothing else changes. Under the corrected Statement the answer is yes: sufficiency is the theorem of Hecke [He22] and Ostrowski [Os27], [Os30] that the site's commentary calls the converse, and necessity is Kesten [Ke66] (Kesten's claim page (1966), accepted, full, refereed). Under the site's wording the answer is no, by Alexeev's Lean disproof, recorded on a claim page (Alexeev, 2026) rejected because it answers the site's wording (both endpoints on the orbit), not the corrected Statement (the length on the orbit), so it does not count toward the problem's standing. The anchored case $u=0$ of the site's wording, that a bounded-discrepancy interval $[0,v)$ has $v=\{\alpha\ell\}$, is true and is the case of Kesten's necessity reconstructed on the theorem page.