Erdős problem 1085 · problems.science

Erdős and Pach showed that, for $d \ge 5$ odd, there exist constants $c_1(d), c_2(d) > 0$ such that $\frac{p - 1}{2p} n^2 - c_1 n^{4/3} ≤ f_d(n) \le \frac{p - 1}{2p} n^2 + c_2 n^{4/3}$ where $p = \lfloor\frac d2\rfloor$ .

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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1085.lean

Retained formal statement3 of 7

Lenz showed that, for $d \ge 4$ , $f_d(n) \ge \frac{p - 1}{2p} n^2 - O(1)$ where $p = \lfloor\frac d2\rfloor$ .

FormalConjectures/ErdosProblems/1085.leanErdos1085.erdos_1085.variants.lower_d4_lenz1 lineExact file

1∀ {d : ℕ}, 4 ≤ d → ∃ C, ∀ (n : ℕ), ↑(d / 2 - 1) / (2 * ↑(d / 2)) * ↑n ^ 2 - C ≤ ↑(Erdos1085.f d n)

SolvedStatement only, no proof

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