Abstract
We study the Diophantine equations obtained by equating a polynomial and the factorial function, and prove the finiteness of integer solutions under certain conditions. For example, we show that there exist only finitely many l such that
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 19J10705
Funding statement: This work was supported by Grant-in-Aid for JSPS Research Fellow (Grant Number: 19J10705).
Acknowledgements
The author deeply expresses their sincere gratitude to Professor M. Ram Murty and Professor Andrzej Dąbrowski for fruitful discussions. The author also deeply thanks Professor Kohji Matsumoto and Professor Masatoshi Suzuki for their precious advice.
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