Erdős Problems

Browse all problems

↑ ↓ to move↵ to openesc to close

Loading problem…

Status

On this page

Status

Topics

Terms Privacy info@plasma.ai

Problem 930 — Erdős Problems

Problem 930

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?

Source: erdosproblems.com/930

Number theory

Wiki page

Status

Open

No claim settles this problem.

Er76d: Erdős, P., Problems and results on number theoretic properties of consecutive integers and related questions. Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975) (1976), 25-44.
ErSe75: Erdős, P. and Selfridge, J. L., The product of consecutive integers is never a power. Illinois J. Math. (1975), 292-301.

Proof claims

Loading proof claims…

Discussion

Loading discussion…

PreviousProblem 929 NextProblem 931

On this page

Statement
Status
References
Proof claims
Discussion

Status: Open
Topics: Number theory
In the wiki: Wiki page