Sobre un criterio de divisibilidad entre once

Margarita Tetlalmatzi-Montiel; Andrés E. Blancas-Saavedra; Benjamín A. Itzá-Ortiz

doi:10.29057/icbi.v8i15.5632

Margarita Tetlalmatzi-Montiel Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0003-3659-1538
Andrés E. Blancas-Saavedra Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0001-8151-5222
Benjamín A. Itzá-Ortiz Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0002-6189-3266

DOI: https://doi.org/10.29057/icbi.v8i15.5632

Keywords: Divisibility, Integer numbers, Palindromic numbers

Abstract

After a brief review of divisibility rules for integer numbers, in this work we present the following simple divisibility rule for 11, which is new as far as the authors are concerned: an integer is divisible by 11 if and only if the sum of the number formed by its last two digits plus the number obtained by deleting those two digits is divisible by 11. Applications and historical notes are also included.

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References

Apostol, T. M., 1976. Introduction to Analytic Number Theory. Springer-Verlag, New York.

Bogomolny, A., 2018. Divisibility by 7, 11, and 13. U´ ltimo acceso 10 de marzode 2020. URL: https://www.cut-the-knot.org/blue/div7-11-13.shtml

Cantor, M., 1880. Vorlesungen ¨uber geschichte der mathematik. Internet Archive. URL: https://archive.org/details/vorlesungenberge02unse/page/8/mode/2up

Dickson, E., 2005. History of the Theory of Numbers. Divisibility and Primality. Vol. 1. Dover, New York.

Kisačanin, B., 2002. Mathematical problems and proof. Combinatorics, number theory and geometry. Kluwer Academic Publisher, New York.

McDowell, E. L., 2018. Divisibility tests: A history and user’s guide. Convergence. DOI: 10.4169/convergence20180513

Niven, I., Zuckerman, H. S., Montgomery, H. L., 1991. An introduction to the theory of numbers. John Wiley & Sons Inc., New York.

Ore, O., 1988. Number theory and its history. Dover, New York.

Preneel, B., Rijmen, V., 1998. Cryptographic primitives for information authentication - state of the art. Lecture Notes in Computer Science 1528, 49–104.

Renault, M., 2006. Stupid divisibility tricks. 101 ways to stupefy your friends. Math Horizons 14 (2), 18–42. DOI: 10.1080/10724117.2006.11974676

Richmond, B., Richmond, T., 2004. A discrete transition to advanced mathematics. Vol. 3. Pure and Applied Undergraduate Texts. American Mathematical

Society, Providence Rhode Island.

Singler, L., 2002. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. Sources and Studies in the History

of Mathematics and Physical Sciences. Springer, New York.

Smith, F., 1971. Divisibility rules for the fifteen primes. The arithmetic teacher 18 (2), 85–87.

Studio Kamada, 2020. Factorization of 11...11 (repunit). U´ ltimo acceso 10 de marzo de 2020. URL: https://stdkmd.net/nrr/repunit/

Wells, D., 1986. The penguin dictionary of curious and interesting numbers. Penguin Books, Great Britain.

Wikipedia, 2020. Divisibility rule. U´ ltimo acceso 10 de marzo de 2020. URL: https://en.wikipedia.org/wiki/Divisibility rule