On factorials which are products of factorials

  title={On factorials which are products of factorials},
  author={Florian Luca},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  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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