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Erdős problem 142 - lower Show that r k ( N ) = o k ( N / log N ) r_k(N) = o_k(N / \log N) r k ( N ) = o k ( N / log N ) , where
the largest possible size of a subset
of
{ 1 , … , N } \{1, \dots, N\} { 1 , … , N } that does not contain any non-trivial
-term arithmetic progression.
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Lean type
∀ (k : ℕ), 1 < k → (fun N => ↑(Erdos142.r k N)) =o[Filter.atTop] fun N => ↑N / Real.log ↑NWhat you must prove
import FormalConjectures.ErdosProblems.«142»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos142.erdos_142.variants.lower" := by
sorry
end Bounty
Pinned source: FormalConjectures/ErdosProblems/142.lean
Source type SHA-256 sha256:a3f73a02f0e943bd284c080928f5a62067c273a79ce4fb3b55dd05a781c9f52c
Task id fc-379fc029-variants-lower-6ff2287ea4-formalized-v1
Task commitment sha256:cf95a04071dd7c65efd5b1aae958c0d2325e29a427d660761cbb7118397da9a9 Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Erdős problem 142 - lower · Conjectures.io