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Modular Arithmetic and Applications

Abstract

In this paper we give an introduction to modular arithmetic. We recall basic notions such as divisibility, greatest common divisor and Bézout's identity. Later we explain some ideas about modular arithmetic and the arithmetic of Zm. To conclude, we provide some easy applications of the modular arithmetic to different fields of mathematics: algebra, criptography and simulation in statistics.

References

D. M. Burton, Elementary Number Theory, 7.a ed. (McGraw Hill, 2010).

T. M. Apostol, Introduction to Analytic Number Theory (Springer, 1976).

S. Singh, Fermat’s Last Theorem (Harper Collins, 1997).

D. H. Lehmer, “Mathematical models in large-scale computing units”, Ann. Comput. Lab. (Harvard University) 26, 141–146 (1951).

E. Castilla y P. J. Chocano, “Introducción al Método de Montecarlo”, Gaceta de la Real Sociedad Matemática Española 26, 87–109 (2023).

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