American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2019, 7(12), 989-993
DOI: 10.12691/education-7-12-14
Open AccessArticle

An Elementary Method in Number Theory

Nguyen Thanh Quang1, and Phan Duc Tuan2

1School of Natural Science Education, Vinh University, Vinh City, Vietnam

2Department of Applied Mathematics, Saigon University, Ho Chi Minh City, Vietnam

Pub. Date: December 30, 2019

Cite this paper:
Nguyen Thanh Quang and Phan Duc Tuan. An Elementary Method in Number Theory. American Journal of Educational Research. 2019; 7(12):989-993. doi: 10.12691/education-7-12-14

Abstract

In order to apply the role of the analogues between integers and polynomials, in this paper we introduce a unified diagram to the Fermat's theorem, Mason's theorem, Davenport's theorem and some arithmetic conjectures. Further, we show some applications of this diagram in teaching and researching on arithmetic. By using this elementary method in number theory, we obtained some results for polynomials and holomorphic functions in case complex and p-adic.

Keywords:
integer polynomial analogue mason's theorem abc conjecture

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References:

[1]  Nguyen Thanh Quang and Phan Duc Tuan (2007), A note on Browkin-Brzezinski’s Conjecture, Int. J. Contemp. Math. Sciences, Vol. 2, pp. 1335-1340.
 
[2]  Nguyen Thanh Quang and Phan Duc Tuan (2008), An Extension of Davenport's Theorem for Functions of Several Variables, International Journal of Algebra, Vol. 2, No. 10, pp. 469-475.
 
[3]  Nguyen Thanh Quang and Phan Duc Tuan (2008), A generalization of the abc Conjecture over Function Fields, Journal of Analysis and Applications, Vol. 6, pp. 69-76.
 
[4]  Phan Duc Tuan, Nguyen Thanh Quang (2016), Picard values and uniqueness p-adic meromorphic functions, Acta Mathematica Vietnammica, Vol. 41, No.4, pp. 563-582.
 
[5]  Phan Duc Tuan, Nguyen Thanh Quang (2016), Differential polynomials and value-sharing, Annales Univ. Sci. Budapest., 45, pp. 23-44.
 
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