Problem Statement
Is there a sequence $1\leq d_1<d_2<\cdots$ with density $1$ such that all products $\prod_{u\leq i\leq v}d_i$ are distinct?
Categories:
Number Theory
Progress
A construction of Selfridge (see [786]) shows that there exists such a sequence of density $>1/e-\epsilon$ for any $\epsilon>0$.See also [786].
Source: erdosproblems.com/421 | Last verified: January 15, 2026