On the equation A!B!=C

We consider the equation in the title in positive integers A,B,C. We give an explicit upper bound for C in terms of the difference k:=B−A. Further, we show that for k≤106 this equation has only one (long known) non-trivial solution, given by 6!7!=10!.

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Bibliographic Details
Published in:Journal of number theory 2018-06, Vol.187, p.160-165
Main Authors: Hajdu, L., Papp, Á., Szakács, T.
Format: Article
Language:English
Subjects:
Primes in intervals
Products of factorials
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Summary:We consider the equation in the title in positive integers A,B,C. We give an explicit upper bound for C in terms of the difference k:=B−A. Further, we show that for k≤106 this equation has only one (long known) non-trivial solution, given by 6!7!=10!.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2017.10.020