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Erdős problem 697

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

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

697.lean

Retained formal statement4 of 4

δ<mα+1m‘\delta < \frac{m ^ \alpha + 1}{m}`. This shows that limm→∞δlim_{m\rightarrow\infty} \delta (m, α\alpha) =0= 0 for α<1\alpha < 1. #TODO: prove this theorem.

FormalConjectures/ErdosProblems/697.leanErdos697.erdos_697.variants.delta_lt1 lineExact file
∀ (m : ℕ) (α : ℝ), Erdos697.δ m α < (↑m ^ α + 1) / ↑m
SolvedStatement only, no proof