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Claim. A. Hildebrand, The divisor function at consecutive integers, Pacific J. Math. 129 (1987), no. 2, 307--319, Theorem 1: for all sufficiently large $x$,

$$\#\{n\le x:\tau(n)=\tau(n+1)\}\gg x(\log\log x)^{-3},$$

so the answer to Problem 946 is yes. The proof combines Heath-Brown's method with an idea of Erdős, Pomerance and Sárközy and a sieve estimate (card). The issue is nominally dated June 1987; the publisher records publication on 1 October 1987, the date this page carries.

Depends on. No page of this wiki (the key lemma is quoted from Heath-Brown's paper).

Acceptance. Refereed: Pacific Journal of Mathematics. The site's PROVED label credits Heath-Brown, so the site's credit is not counted as review of this paper.