Skip to content

Erdős problem 1085

Start work

Erdős and Pach showed that, for d≥5d \ge 5 odd, there exist constants c1(d),c2(d)>0c_1(d), c_2(d) > 0 such that p−12pn2−c1n4/3≤fd(n)≤p−12pn2+c2n4/3\frac{p - 1}{2p} n^2 - c_1 n^{4/3} ≤ f_d(n) \le \frac{p - 1}{2p} n^2 + c_2 n^{4/3} where p=⌊d2⌋p = \lfloor\frac d2\rfloor.

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

1085.lean

Retained formal statement3 of 7

Lenz showed that, for d≥4d \ge 4, fd(n)≥p−12pn2−O(1)f_d(n) \ge \frac{p - 1}{2p} n^2 - O(1) where p=⌊d2⌋p = \lfloor\frac d2\rfloor.

FormalConjectures/ErdosProblems/1085.leanErdos1085.erdos_1085.variants.lower_d4_lenz1 lineExact file
∀ {d : ℕ}, 4 ≤ d → ∃ C, ∀ (n : ℕ), ↑(d / 2 - 1) / (2 * ↑(d / 2)) * ↑n ^ 2 - C ≤ ↑(Erdos1085.f d n)
SolvedStatement only, no proof