# On factorials which are products of factorials

@article{Luca2007OnFW,
title={On factorials which are products of factorials},
author={Florian Luca},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
year={2007},
volume={143},
pages={533 - 542}
}
• F. Luca
• Published 1 November 2007
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
Abstract In this paper, we look at the Diophantine equation (0.1)$n!=\prod_{i=1}^t a_i!\qquad n>a_1\ge a_2\ge \cdots\ge a_t\ge 2.$ Under the ABC conjecture, we show that it has only finitely many nontrivial solutions. Unconditionally, we show that the set of n for which the above equation admits an integer solution a1,. . .,at is of asymptotic density zero.
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