Let $A\subset \mathbb{N}$ be infinite. Must there exist some $k\ge 1$ such that almost all integers have a divisor of the form $a+k$ for some $a\in A$?

Worked, still open.

number theory · solved · formalized (Lean) · 0 attempts

machinery: Behrend-sequence,set-of-multiples,density-of-multiples,divisor-in-prescribed-set,covering-system,CRT-construction,Davenport-Erdos,unit-fractions,prime-distribution