The product of consecutive integers cannot be a power (after Erdős and Selfridge), but products of disjoint blocks of consecutive integers can be powers. Even if the blocks have a fixed length l ≥ 4 there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below x.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-1,
author = {Mariusz Ska\l ba},
title = {Products of disjoint blocks of consecutive integers which are powers},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {1-3},
zbl = {1059.11030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-1}
}
Mariusz Skałba. Products of disjoint blocks of consecutive integers which are powers. Colloquium Mathematicae, Tome 96 (2003) pp. 1-3. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-1/