Erdős problem 1056 · problems.science

Let $k ≥ 2$ . Does there exist a prime $p$ and consecutive intervals $I_0,\dots,I_k$ such that $\prod\limits_{n{\in}I_i}n \equiv 1 \mod n$ for all $1 \le i \le k$ ?

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1056.lean

Retained formal statement4 of 4

Noll and Simmons asked, more generally, whether there are solutions to $q_1! \equiv \dots \equiv q_k! \mod p$ for arbitrarily large $k$ (with $q_1 < \dots < q_k$ ).

FormalConjectures/ErdosProblems/1056.leanErdos1056.erdos_1056.variants.noll_simmons6 linesExact file

1True ↔2  ∀ᶠ (k : ℕ) in Filter.atTop,3    ∃ p,4      ∃ (_ : Nat.Prime p),5        ∃ Q,6          ∃ (_ : StrictMono Q) (_ : ∀ (i : Fin k), Q i < p), ∀ (i j : Fin k), (Q i).factorial ≡ (Q j).factorial [MOD p]

OpenStatement only, no proof

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