On the Generators of the Group of Units Modulo a Prime and Its Analytic and Probabilistic Views

Authors

DOI:

https://doi.org/10.32871/rmrj2109.02.03

Keywords:

Generators of (Zp)* ,, Simulation algorithm, Group of units modulo a prime p, (Zp)*

Abstract

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Author Biography

Ricky B. Villeta, University of San Jose-Recoletos, Cebu City, Philippines

Ricky B. Villeta graduated from Mindanao State University – Iligan Institute of Technology (MSU-IIT) with a degree of Bachelor of Science in Mathematics (Pure Mathematics) in 2003 as a fulltime scholar, City Mayor’s scholar (Iligan City) granted from having graduated in high school as class valedictorian and CHED-COE (Center of Excellence in Mathematics) scholar awarded by MSU-IIT mathematics and statistics department. He also obtained his Master of Science in Mathematics degree in 2007, with a specialization in abstract algebra (group theory) at MSU-IIT. He had served as Mathematics Lecturer from 2003 to 2005 and as graduate teaching assistant from 2005 to 2006 at the Mathematics and Statistics Department of the College of Science and Mathematics of MSU-IIT. Since 2006 to present, he is a faculty member of the Department of Mathematics and Sciences of the College of Arts and Sciences at University of San Jose – Recoletos (USJ-R), Cebu City. He has been teaching research methods, design of experiments and statistical models in the graduate school, differential equation, differential calculus, integral calculus, applied statistics in business, behavioral statistics, biostatistics, computer aided analysis, linear algebra, abstract algebra, number theory, probability theory, quantitative analysis in business, mathematical investigations and modeling, among others. He is also a trainer for basic and tertiary non-deped teachers on senior high curriculum in mathematics, statistics and probability areas in the Visayas region. His research works and interests are in abstract algebra (group theory), graph theory, differential equation, mathematical modeling and simulation, fractal statistics, data mining and theory development. He also serves as researcher and research statistician at the Center for Policy, Research and Development Studies in USJ-R.  

References

Adamski, T., & Nowakowski, W. (2015). The
average time complexity of probabilistic
algorithms for finding generators in finite
cyclic groups. Bulletin of the Polish Academy
of Sciences,Technical Sciences, 63(4), 989-996.
https://doi.org/10.1515/bpasts-2015-0112

Burton, D. M., (2007). Elementary number theory
(6thed.). McGraw-Hill.

Gauss, C. F. (1966). Disquisitiones arithmeticae
(English ed). Springer-Verlag.
https://doi.org/10.1007/978-1-4939-7560-0

Knuth, D. E. (1998). The art of computer programming:
Vol. 2. Seminumerical algorithms (3rd ed.).
Addison-Wesley.

Rabin, M. O. (1980). Probabilistic algorithm for
testing primality. Journal of Number Theory, 12(1), 128-138.
https://doi.org/10.1016/0022-314X(80)90084-0

Vinogradov, I. M. (2003). Elements of number theory.
Dover Publications Inc. https://books.google.
com.ph/books?id=xlIfdGPM9t4C&printsec=fr
ontcover#v=onepage&q&f=false

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Published

2021-12-01

How to Cite

Villeta, R. B., Castillano, E. C., & Padua, R. N. (2021). On the Generators of the Group of Units Modulo a Prime and Its Analytic and Probabilistic Views. Recoletos Multidisciplinary Research Journal, 9(2), 115–121. https://doi.org/10.32871/rmrj2109.02.03

Issue

Vol. 9 No. 2 (2021)

Section

Articles

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Copyright of the Journal belongs to the University of San Jose-Recoletos

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