Erdős problem 697 · problems.science

For each $m$ and $\alpha$ , the density of the set of integers which are divisible by some $d \equiv 1 \pmod{m}$ with $1 < d < \exp (m ^ \alpha)$ exists.

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FormalConjectures/ErdosProblems/

697.lean

Retained formal statement4 of 4

$\delta < \frac{m ^ \alpha + 1}{m}`$ . This shows that $lim_{m\rightarrow\infty} \delta$ (m, $\alpha$ ) $= 0$ for $\alpha < 1$ . #TODO: prove this theorem.

FormalConjectures/ErdosProblems/697.leanErdos697.erdos_697.variants.delta_lt1 lineExact file

1∀ (m : ℕ) (α : ℝ), Erdos697.δ m α < (↑m ^ α + 1) / ↑m

SolvedStatement only, no proof

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