p adic introduction without algebra prerequisite?

Question

Is there a p-adic introduction, focusing on the simple number theory, without prerequisite of algebra knowledge such as group/field etc?

Answer 1

Some elementary references I know of are:

[1] Farhad Bill Aslan and Howard Becton Duck, The real number system vs. a system called $10$-adic, School Science and Mathematics 92 #8 (December 1992), pp. 427−432.

Summary at ERIC.

[2] Boris Mikhailovich Bekker, Sergei Vladimirovich Vostokov, and Yury J. Ionin, $2$-adic numbers, Quantum 9 #6 (July−August 1999), pp. 22−26.

A slightly revised reprint of this 1999 paper was published as Chapter 2 (pp. 99−109) in Serge Lwowitsch Tabachnikov (editor), Kvant Selecta: Algebra and Analysis, I, Mathematical World #14, American Mathematical Society, 1999. The book chapter is nearly identical except that it includes a solution (attributed to Dmitry Konstantinovich Faddeev) to the problem stated at the beginning of the section titled The $2$-adic Logarithm.

[3] Edward Bruce Burger and Thomas Struppeck, Does $\Sigma_{n=0}^{\infty}\frac{1}{n!}$ really converge? Infinite series and $p$-adic analysis, American Mathematical Monthly 103 #7 (August−September 1996), pp. 565−577.

[4] Albert [Al] Anthony Cuoco, Making a divergent series converge, Mathematics Teacher 77 #9 (December 1984), pp. 715−717.

[5] Cyrus Colton MacDuffee, The $p$-adic numbers of Hensel, American Mathematical Monthly 45 #8 (October 1938), pp. 500−508.

[6] Ilya Shevelevich Slavutskii, First steps in the geometry of $p$-adic fields, Mathematical Spectrum 28 #3 (May 1996), pp. 54−55.