Erdős problem 137

Let $k\geq 3$ . Can the product of any $k$ consecutive integers $N$ ever be powerful? That is, must there always exist a prime $p\mid N$ such that $p^2\nmid N$ ?

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

Open selected source

FormalConjectures/ErdosProblems/

137.lean

Retained formal statement1 of 3

Let $k\geq 3$ . Can the product of any $k$ consecutive integers $N$ ever be powerful? That is, must there always exist a prime $p\mid N$ such that $p^2\nmid N$ ?

FormalConjectures/ErdosProblems/137.leanErdos137.erdos_1371 lineExact file

1sorry ↔ ∀ k ≥ 3, ∀ (n : ℕ), ¬(∏ x ∈ Finset.Ioc n (n + k), x).Powerful

OpenStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures3
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
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/
  - 137.lean3