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

FormalConjectures/ErdosProblems/

137.lean

Retained formal statement3 of 3

Let $k\geq 2$ . Erdős and Selfridge [ES75] proved that the product of any $k$ consecutive integers $N$ cannot be a perfect power.

[ES75] P. Erdös, J. L. Selfridge, "The product of consecutive integers is never a power", Illinois J. Math. 19(2): 292-301, 1975

FormalConjectures/ErdosProblems/137.leanErdos137.erdos_137.variants.perfect_power1 lineExact file

1∀ k ≥ 2, ∀ (n x l : ℕ), 2 ≤ l → ∏ x ∈ Finset.Ioc n (n + k), x ≠ x ^ l

SolvedStatement only, no proof