论文标题
Brocard-Ramanujan问题的一些结果在Diophantine方程式上$ n！+1 = m^2 $
Some results of Brocard-Ramanujan problem on diophantine equation $n!+1=m^2$
论文作者
论文摘要
Brocard-Ramanujan问题与Diophantine方程有关$ n！+1 = m^2 $，一个著名的未解决问题，涉及寻找方程的整数解决方案。尽管我们许多人已经尝试过，但没有人发现超过$ n = 4，〜5 $和7美元的问题的任何新解决方案。布鲁斯·伯恩特（Bruce Berndt）和威廉·戈尔韦（William Galway）\ cite {berndt}在2000年没有通过广泛的计算机搜索$ n $ $ n $ 10^9 $的解决方案找到任何新解决方案。这项研究的主要目的是表明该解决方案应满足一些必要和/或足够的条件，并且它只有有限的许多解决方案，这些解决方案并非基于对Brocard-Ramanujan问题的任何猜想或先前的研究。
The Brocard-Ramanujan problem pertaining to the diophantine equation $n!+1=m^2$, a famously unsolved problem, deals with finding the integer solutions to the equation. Nobody has discovered any new solution of the problem beyond $n=4,~5$ and $7$ although many of us have tried it. Bruce Berndt and William Galway \cite{Berndt} had not found any new solution in 2000 by extensive computer search for a solution with $n$ up to $10^9$. The main purpose of this study is to show that the solutions should satisfy some necessary and/or sufficient conditions and it has only finitely many solutions which is not based on any conjecture or previous research on the Brocard-Ramanujan problem.
