On the finiteness of solutions for polynomial-factorial Diophantine equations
On the finiteness of solutions for polynomial-factorial Diophantine equations
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>l</m:mi> <m:mo lspace="0pt" rspace="3.5pt">!</m:mo> </m:mrow> </m:math> {l!} is represented …