Problem #826: Are there infinitely many $n$ such that, for all $k\geq...

Are there infinitely many $n$ such that, for all $k\geq 1$,\[\tau(n+k)\ll k?\]

SOLVED

Problem Statement

Are there infinitely many $n$ such that, for all $k\geq 1$,\[\tau(n+k)\ll k?\]

Categories: Number Theory

A stronger form of [248].

Source: erdosproblems.com/826 | Last verified: January 16, 2026