eng Science and Education Publishing American Journal of Educational Research 2327-6150 2019-12-30 7 12 989 993 10.12691/education-7-12-14 EDUCATION201971214 article Nguyen Thanh Quang ntquangdhv@gmail.com 1 Phan Duc Tuan 2 School of Natural Science Education, Vinh University, Vinh City, Vietnam Department of Applied Mathematics, Saigon University, Ho Chi Minh City, Vietnam 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. http://pubs.sciepub.com/education/7/12/14/education-7-12-14.pdf integer polynomial analogue mason's theorem abc conjecture