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Finiteness of trivial solutions of factorial products yielding a factorial over number fields

Volume 190 / 2019

Wataru Takeda Acta Arithmetica 190 (2019), 395-401 MSC: Primary 11D45; Secondary 11D57, 11D72. DOI: 10.4064/aa181010-29-1 Published online: 23 July 2019


We consider a Bertrand type estimate for primes splitting completely. As one of its applications, we show the finiteness of the set of trivial solutions of a Diophantine equation involving the factorial function over number fields other than the rational number field.


  • Wataru TakedaDepartment of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan

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