Peculiarities of smoothly undulating number

Authors

DOI:

https://doi.org/10.22481/intermaths.v4i2.13906

Keywords:

divisibility, undulating numbers, primality

Abstract

This notes presents results related to divisibility or multiplicity between two numbers in the class of integers called  smoothly undulating numbers of the type uz[n]. The main result is to characterize and display types of divisors of some types of numbers uz[n], and we show an algorithm to determine the greatest common divisor between two numbers uz[n].

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References

C. A. Pickover . “Is There a Double Smoothly Undulating Integer?”, Journal of Recreational Mathematics , v.22, n.1, p. 52-53, 1990.

C. A. Pickover. Keys to Infinity (Chapter 20). New York, 1995.

C. A. Pickover. Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning . (Chapter 52 and 88). Oxford University Press, 2003.

D. F. Robinson. “There are no double smoothly undulating integers in both decimal and binary representation”. Journal of Recreational Mathematics , v. 26, n. 2, p. 102-103, 1994.

K. Shirriff. “Comments on Double Smoothly Undulating Integers”. Journal of Recreational Mathematics , v. 26, n. 2, p. 103-104, 1994.

E. A. Costa; G. A. Costa, G. A. “Existem números primos na forma 101... 01”. Revista do Professor de Matemática , n. 103, p. 21-22, 2021.

F. S. Carvalho, ; E.A. Costa. “Um passeio pelos números ondulantes”. REMAT: Revista Eletrônica da Matemática, v. 8, n. 2, p. e3001-e3001, 2022. https://doi.org/10.35819/remat2022v8i2id6043

P. Ribenboim. The little book of bigger primes. 2nd ed. New York: Springer, 2004.

A. Hefez. Aritmética . SBM-Coleção PROFMAT, 2a. ed. Rio de Janeiro-RJ. SBM, 2016.

I. Niven; H.S. Zuckerman; H. L. Montegomery. An introduction to the theory of numbers . John Wiley and Sons. 1991.

E. A. Costa; A. B. Souza. “Números ondulantes na forma 101...01”. Gazeta Matemática , SPM, 2024 (a aparecer).

A. H. Beiler. Recreations in the theory of numbers: the queen of mathematics entertains. 2nd ed. New York: Dover, 1966.

E. A. Costa; D. C. Santos. “Algumas propriedades sobre os números Monodígitos e Repunidades”. Revista de Matemática , v. 2, p. 47-58, 2022.

S. Yates. Repunits and repetends. Star Publishing Co., Inc. Boynton Beach, Florida, 1992.

C. G. T. de Moreira; F. E. B. Martinez; N. C. Saldanha. Tópicos de teoria dos números. Rio de Janeiro: SBM, 2012.

L. Maohua. “A note on perfect powers of the form xm−1 + . . . + x + 1”. Acta Arithmetica, v. 69, n. 1, p. 91-98, 1995.

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Published

2023-12-30

How to Cite

Santos, D. C., & Costa, E. A. . (2023). Peculiarities of smoothly undulating number. INTERMATHS, 4(2), 38-53. https://doi.org/10.22481/intermaths.v4i2.13906

Issue

Vol. 4 No. 2 (2023)

Section

Artigos

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