Erdős problem 930 · problems.science

Is it true that, for every $r$ , there is a $k$ such that if $I_1,\ldots,I_r$ are disjoint intervals of consecutive integers, all of length at least $k$ , then $\prod_{1\leq i\leq r}\prod_{m\in I_i}m$ is not a perfect power?

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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

930.lean

Retained formal statement2 of 3

Erdos and Selfridge [ErSe75] proved that the product of consecutive integers is never a power (establishing the case $r=1$ ).

Theorem 1 from [ErSe75].

It is implied from erdos_930.variants.consecutive_strong.

[ErSe75] Erdős, P. and Selfridge, J. L., The product of consecutive integers is never a power. Illinois J. Math. (1975), 292-301.

FormalConjectures/ErdosProblems/930.leanErdos930.erdos_930.variants.consecutive_integers1 lineExact file

1∀ (n k : ℕ), 0 ≤ n → 2 ≤ k → ¬Erdos930.IsPower (∏ m ∈ Finset.Icc (n + 1) (n + k), m)

SolvedStatement only, no proof

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