Erdős problem 1192

Does there exist, for all $r\geq 2$ , a basis $A$ of order $r$ (so that $f_r(n)>0$ for all large $n$ ) such that $\sum_{n\leq x}f_r(n)^2 \ll x$ for all $x$ ?

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

1192.lean

Retained formal statement7 of 7

Ruzsa [Ru90] proved that the answer is yes for $r=2$ .

FormalConjectures/ErdosProblems/1192.leanErdos1192.erdos_1192.variants.ruzsa3 linesExact file

1∃ A,2  (∀ᶠ (n : ℕ) in Filter.atTop, Erdos1192.f_r A 2 n > 0) ∧3    (fun x => ∑ n ∈ Finset.range (x + 1), ↑(Erdos1192.f_r A 2 n) ^ 2) =O[Filter.atTop] fun x => ↑x

SolvedStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures7
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 1192.lean7