feat(ErdosProblems): 683 #1533
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feat(ErdosProblems): 683 #1533
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YaelDillies
reviewed
Jan 8, 2026
YaelDillies
added
ams-11: Number theory
awaiting-author
Member
|
Could you state https://www.erdosproblems.com/961 simultaneously? |
Collaborator
Author
Do you mean something like /--
Erdos 961 is equivalent to Erdos 683.
-/
@[category research solved, AMS 11]
theorem erdos_683_equiv_erdos_961 :
(∃ c > 0, ∀ n k : ℕ, 0 < k ∧ k < n → P n k > min (n - k + 1) (k ^ (1 + c))) ↔
(∃ C > 0, ∀ᶠ k in atTop, f k < (log (k : ℝ)) ^ C) := by
sorryafter importing Erdos961? |
Member
|
I was thinking you could prove one in terms of the other |
smmercuri
reviewed
Jan 21, 2026
| -/ | ||
| @[category research open, AMS 11] | ||
| theorem erdos_683 : answer(sorry) ↔ | ||
| (∃ c > 0, ∀ n k : ℕ, 0 < k ∧ k < n → P n k > min (n - k + 1) (k ^ (1 + c))) := by |
Collaborator
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I think c should have type ℝ here (currently it's ℕ). Similarly below
| -/ | ||
| @[category research open, AMS 11] | ||
| theorem erdos_683 : answer(sorry) ↔ | ||
| (∃ c > 0, ∀ n k : ℕ, 0 < k ∧ k < n → P n k > min (n - k + 1) (k ^ (1 + c))) := by |
Collaborator
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The informal has le here instead of lt
Suggested change
| (∃ c > 0, ∀ n k : ℕ, 0 < k ∧ k < n → P n k > min (n - k + 1) (k ^ (1 + c))) := by | |
| (∃ c > 0, ∀ n k : ℕ, 0 ≤ k ∧ k ≤ n → P n k > min (n - k + 1) (k ^ (1 + c))) := by |
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Closes #876