论文标题
Narayana序列和Brocard-Ramanujan方程
Narayana Sequence and The Brocard-Ramanujan Equation
论文作者
论文摘要
令$ \ left \ lbrace a_ {n} \ right \ rbrace_ {n \ geq 0} $是由recurence $ a_ {n} = a_ {n-1}+a_ {n-3} $的narayana序列定义的narayana序列。 $ a_ {1} = a_ {2} = 1 $。 In This paper, we fully characterize the $3-$adic valuation of $a_{n}+1$ and $a_{n}-1$ and then we prove that there are no integer solutions $(u,m)$ to the Brocard-Ramanujan Equation $m!+1=u^2$ where $u$ is a Narayana number.
Let $\left\lbrace a_{n}\right\rbrace_{n\geq 0}$ be the Narayana Sequence defined by the recurence $a_{n}=a_{n-1}+a_{n-3}$ for all $n\geq 3$ with intital values $a_{0}=0$ and $a_{1}=a_{2}=1$. In This paper, we fully characterize the $3-$adic valuation of $a_{n}+1$ and $a_{n}-1$ and then we prove that there are no integer solutions $(u,m)$ to the Brocard-Ramanujan Equation $m!+1=u^2$ where $u$ is a Narayana number.
