Erdős problem 244 · problems.science

Let $C > 1$ . Does the set of integers of the form $p + \lfloor C^k \rfloor$ , for some prime $p$ and $k\geq 0$ , have density $>0$ ?

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2 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

244.lean

Retained formal statement2 of 2

Romanoff [Ro34] proved that the answer is yes if $C$ is an integer.

[Ro34] Romanoff, N. P., _Über einige Sätze der additiven Zahlentheorie_. Math. Ann. (1934), 668-678.

FormalConjectures/ErdosProblems/244.leanErdos244.erdos_244.variants.Romanoff1 lineExact file

1∀ {C : ℕ}, 1 < C → 0 < {x | ∃ p k, ∃ (_ : Nat.Prime p), p + ⌊C ^ k⌋₊ = x}.lowerDensity

SolvedStatement only, no proof