Pinner's equal divisor counts at every fixed shift

Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Claim. C. G. Pinner, Repeated values of the divisor function, Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 192, 499--502, proves that for every positive integer $B$ there are infinitely many $n$ with $\tau(n)=\tau(n+B)$ ; at $B=1$ this answers Problem 946 yes. The zbMATH review (Zbl 0890.11028) states the theorem in this form and says that the extension of Heath-Brown's method needs further care with the prime divisors of $B$ . The issue is dated December 1997 and no day is given, so this page carries the first of that month.

Depends on. No page of this wiki.

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

Linked from (3)

Problem 946 Heath-Brown's infinitely many equal divisor counts at n and n plus 1 problems/divisors/E0946/claims

Graph