Erdős problem 955

If $A\subset \mathbb{N}$ has density $0$ then $s^{-1}(A)$ must also have density $0$ .

Sources

The source's own material, retained exactly.

12 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

955.lean

Retained formal statement7 of 12

Troupe [Tr15] has shown that this is true if $A$ is the set of integers with unusually many prime factors.

FormalConjectures/ErdosProblems/955.leanErdos955.erdos_955.variants.troupe_unusually_many_prime_factors5 linesExact file

1∀ ε > 0,2  {x |3        (1 + ε) * Real.log (Real.log ↑(Erdos955.s x)) <4          ↑(ArithmeticFunction.cardDistinctFactors (Erdos955.s x))}.HasDensity5    0

SolvedStatement only, no proof