Erdős problem 1056

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 $1 \le i \le k$ ?

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1056.lean

Retained formal statement2 of 4

This is problem A15 in Guy's collection [Gu04], where he reports that in a letter in 1979 Erdős observed that $3 * 4 \equiv 5 * 6 * 7 \equiv 1 \mod 11$ .

FormalConjectures/ErdosProblems/1056.leanErdos1056.erdos_1056.variants.k21 lineExact file

1Erdos1056.AllModProdEqualsOne 11 ![3, 5, 8]

TextbookStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures4
statement retained
VibeMathed0
not observed here
PLBY Lean proofs1
no statement retained
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 1056.lean4