在這篇論文中，我們回顧一些p進數分析中的性質以及對階層在p進範數下的收斂問題到目前為止所提出過的相關結果，並整理一些可能可行的想法以及與其相關的問題。

In this paper, we review some properties in p-adic analysis, and the outcomes provided to this n-factorial convergence problem so far. Also we organize some possible ideas and related problems.

1.Introduction...1
1.1 Background...1
1.2 P-adic Sequences and Series...3
2.Factorial in P-adic Field...5
2.1 Factorial Sum...5
2.2 Rationality of P-adic Numbers...7
2.3 Expansion of Sum of Series...9
3 Possible Ideas and Related Problems...11
3.1 Possible Ideas:In Analytic and Algebraic Approach...11
3.2 Related Problems...13
Appendices...15
I Construction of Qp...15
Reference...17

1.N.Koblitz. p-adic Numbers, p-adic Analysis, and Zeta-Functions. Springer-Verlag, New York, 2nd Ed(1984).

2.K.Mahler. p-adic Numbers and Their Functions. Cambridge Press,2nd Ed (1981).

3.Hermite. Open Problems With Factorials.
Universitat Politècnica de Catalunya(2018).

4.W.H.Schikhof. Ultrametric Calculus, An Introduction to p-adic Analysis. Cambridge Studies in Adv. Math.4, Cambridge University Press(1984).

5.J.Neukirch. Algebraic Number Theory. Springer-Verlag , Berlin , Heidelberg(1999).

6.A.M.Robert. A Course in p-adic Analysis. Springer-Verlag, New York(2000).

7.K.Conrad . Infinite series in p-adic fields. https://kconrad.math.uconn.edu/ blurbs/gradnumthy/infseriespadic.pdf.

8.B.Dragovich, N.Z.Misic. p-Adic Invariant Summation of Some p-Adic Functional Series, arXiv:1411.4195(2014)

9.A.A.Shaikh, M.A.Sarkar. On convergence and rational summation of power series in p-adic field, vol 9 arXiv:1809.07705(2019).