Back to Problems

erdos_252.schinzel

Specification

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

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
theorem erdos_252.schinzel (hs : ∀ (fs : Finset (Polynomial ℤ)), (∀ f ∈ fs, BunyakovskyCondition f)
    → SchinzelCondition fs → Infinite ↑{n | ∀ f ∈ fs, Prime (Polynomial.eval (↑n) f).natAbs}) :
    ∀ k, Irrational (∑' n, σ k n / (n ! : ℝ))
ID: ErdosProblems__252__erdos_252.schinzel
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.