Let denote the ith prime. We conjecture that there are precisely 28 solutions to the equation in positive integers n and α₁,..., . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-7,
author = {Andrzej D\k abrowski},
title = {On the Brocard-Ramanujan problem and generalizations},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {105-110},
zbl = {1308.11039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-7}
}
Andrzej Dąbrowski. On the Brocard-Ramanujan problem and generalizations. Colloquium Mathematicae, Tome 126 (2012) pp. 105-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-7/