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 statement3 of 4

Makowski [Ma83] found, for $k=3$ : $2 * 3 * 4 * 5 \equiv 6 * 7 * 8 * 9 * 10 * 11 \equiv 12 * 13 * 14 * 15 \equiv 1 \mod 17$ .

FormalConjectures/ErdosProblems/1056.leanErdos1056.erdos_1056.variants.k31 lineExact file

1Erdos1056.AllModProdEqualsOne 17 ![2, 6, 12, 16]

TextbookStatement only, no proof