Erdős problem 252 · problems.science

Erdős Problem 252: irrationality of the sum for a given $k$ .

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FormalConjectures/ErdosProblems/

252.lean

Retained formal statement9 of 9

If Schinzel's conjecture is true, then ∑ σ k n / n! is irrational for all k. This is proved in [ScPu06].

FormalConjectures/ErdosProblems/252.leanErdos252.erdos_252.variants.schinzel4 linesExact file

1(∀ (fs : Finset (Polynomial ℤ)),2    (∀ f ∈ fs, BunyakovskyCondition f) →3      SchinzelCondition fs → Infinite ↑{n | ∀ f ∈ fs, Prime (Polynomial.eval n f).natAbs}) →4  ∀ (k : ℕ), Irrational (Erdos252.erdos_252_sum k)

SolvedStatement only, no proof

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