与阶乘有关的丢番图方程sum from k=1 to n k!=q^m+a

Diophantine Equation Concerning Factorials sum from k=1 to n k!=q^m+a

与阶乘有关的高次丢番图方程,一直是数论中引人关注的课题。文章研究了方程sum from k=1 to n k!=q^m+a,利用阶乘的有关性质,求出了以上方程当a=±1,-2,±4时的全部整数解,并提出了一些猜想。

The higher Diophantine equations is very important in number theory. In this paper, we study the Diophantine equations concerning factorials n∑k=1k!=q^m＋a, and the equation are solved when a=±1,-2,±4.