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Journal articles on the topic 'Smarandache conjecture'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Li, Xiumei, and Min Sha. "A Proof of Sondow’s Conjecture on the Smarandache Function." American Mathematical Monthly 127, no. 10 (2020): 939–43. http://dx.doi.org/10.1080/00029890.2020.1820789.

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2

Li, Mu Chun, Shuang Li Wang, and Li Li Wang. "The Smarandachely Adjacent Vertex Distinguishing E-Total Coloring of some Join Graphs." Applied Mechanics and Materials 475-476 (December 2013): 379–82. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.379.

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Using the analysis method and the function of constructing the Smarandachely adjacent vertex distinguishing E-total coloring function, the Smarandachely adjacent vertex distinguishing E-total coloring of join graphs are mainly discussed, and the Smarandachely adjacent vertex distinguishing E-total chromatic number of join graph are obtained. The Smarandachely adjacent vertex distinguishing E-total coloring conjecture is further validated.

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3

.., Victor, and Robert N. Boyd. "Remark on Recent Experimental Findings supporting Smarandache’s Quantum Sorites Paradoxes, Superluminal Hypothesis, and SubQuantum Kinetic Model of Electron." Journal of Cosmology, Filaments and Astrobiology 1, no. 1 (2022): 08–15. http://dx.doi.org/10.54216/jcfa.010101.

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Statement of the Problem: Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen (EPR) paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic Model of Elect

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4

Octavian, Cira. "Smarandache’s Conjecture on Consecutive Primes." April 17, 2014. https://doi.org/10.5281/zenodo.23259.

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5

Luca, Florian. "On the Smarandache Irrationality Conjecture." August 10, 2011. https://doi.org/10.5281/zenodo.9651.

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6

Russo, Felice. "Some results about four Smarandache U-product sequences." April 1, 1999. https://doi.org/10.5281/zenodo.9039.

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In this paper four Smarandache product sequences have been studied: Smarandache Square product sequence, Smarandache Cubic product sequence, Smarandache Factorial product sequence and Smarandache Palprime product sequence. In particular the number of primes, the convergence value for Smarandache Series, Smarandache Continued Fractions, Smarandache Infinite product of the mentioned sequences has been calculated utilizing the Ubasic software package. Moreover for the first time the notion of Smarandache Continued Radicals has been introduced. One conjecture about th

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7

Octavian, Cira. "Smarandache's Conjecture on Consecutive Primes." November 30, 2014. https://doi.org/10.5281/zenodo.826647.

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8

Wang, Yang, and Hong Li Zhang. "On a Conjecture of F. Smarandache." May 21, 1995. https://doi.org/10.5281/zenodo.8924.

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9

Prodanescu, I., and L. Tutescu. "ON A CONJECTURE CONCERNING THE SMARANDACHE FUNCTION." September 30, 1995. https://doi.org/10.5281/zenodo.8923.

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10

Ashbacher, Charles. "On A Conjecture By Russo." September 23, 1999. https://doi.org/10.5281/zenodo.8921.

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11

Le, Maohua. "ON THE THIRD SMARANDACHE CONJECTURE ABOUT PRIMES." May 2, 2001. https://doi.org/10.5281/zenodo.9086.

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12

Saidak, F. "Erdos Conjecture I." May 22, 2000. https://doi.org/10.5281/zenodo.8969.

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In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of the distribution of primes in various special forms, paying a brief attention to Fermat, Mersenne, Fibonacci, Lucas and Smarandache sequences, and I debate some side effects of the most surprising results it implies. At the end I also give connections of the questions discussed to other important areas o

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13

Russo, Felice. "An experimental evidence on the validity of third Smarandache conjecture on primes." February 24, 2001. https://doi.org/10.5281/zenodo.8982.

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14

Yuan, Yi. "THE 97-TH PROBLEM OF F. SMARANDACHE." December 10, 1999. https://doi.org/10.5281/zenodo.8775.

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15

Yani, Zheng. "On the Pseudo Smarandache function and its two conjectures." August 31, 2007. https://doi.org/10.5281/zenodo.853058.

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16

Coman, Marius. "Conjecture that relates both the lesser and the larger term of a pair of twin primes to the same number through two different functions." September 5, 2010. https://doi.org/10.5281/zenodo.22867.

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In this paper I conjecture that for any pair of twin primes p and p + 2 there exist an odd positive integer n such that the value of Smarandache function for n is equal to p and the value of MC function for n is equal to p + 2.

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17

Mao, Linfan. "Sequences on Graphs with Symmetries." September 24, 2011. https://doi.org/10.5281/zenodo.9623.

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An interesting symmetry on multiplication of numbers found by Prof.Smarandache recently. By considering integers or elements in groups on graphs, we extend this symmetry on graphs and find geometrical symmetries. For extending further, Smarandache’s or combinatorial systems are also discussed in this paper, particularly, the CC conjecture presented by myself six years ago, which enables one to construct more symmetrical systems in mathematical sciences.

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18

Octavian, Cira. "Conjectura Smarandache." January 26, 2014. https://doi.org/10.5281/zenodo.32305.

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19

Russo, Felice. "On some Smarandache conjectures and unsolved problems." May 23, 1995. https://doi.org/10.5281/zenodo.9586.

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20

Begay., A. "SMARANDACHE CEIL FUNCTIONS." December 12, 2007. https://doi.org/10.5281/zenodo.9579.

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In this paper some defmitions, examples and conjectures are exposed related to the Smarandache type functions, found in the Archives of the Arizona State University, Tempe, USA Special Collections.

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21

Karama, Muneer Jebreel. "Smarandache inversion sequence." February 2, 2006. https://doi.org/10.5281/zenodo.9650.

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We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System.

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22

Perez, L. "PRIM-SUM." August 24, 1998. https://doi.org/10.5281/zenodo.9505.

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23

Karama, Muneer Jebreel. "Smarandache Concatenated Magic Squares." August 9, 2001. https://doi.org/10.5281/zenodo.9660.

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24

Karama, Muneer Jebreel. "SMARANDACHE FRIENDLY CUBE NUMBERS." April 15, 2006. https://doi.org/10.5281/zenodo.9085.

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The main purpose of this paper is to introduce new concepts of Smarandache numbers, namely Smarandache Friendly Cube Numbers, and give definitions, curious note, theorem, conjectures, proposed future studies, and ask open problems.

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25

Wenpeng, Zhang, and Li Ling. "Two problems related to the Smarandache function." September 5, 2008. https://doi.org/10.5281/zenodo.854342.

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The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n) and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures.

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26

Wenpeng, Zhang, and Ling Li. "Two problems related to the Smarandache function." May 2, 2008. https://doi.org/10.5281/zenodo.8768.

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The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n) and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures.

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27

Bencze, M. "SMARANDACHE RELATIONSHIPS AND SUBSEQUENCES." May 1, 2014. https://doi.org/10.5281/zenodo.9210.

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Some Smarandache relationships between the terms of a given sequenceare studied in the fIrst paragraph. In the second paragraph, are studied Smarandache subsequences (whose terms have the same property as the initial sequence). In the third paragraph are studied the Smarandache magic squares and cubes of order n and some conjectures in number theory.

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28

Maohua, Le. "ON THE PSEUDO-SMARANDACHE SQUAREFREE FUNCTION." July 4, 2006. https://doi.org/10.5281/zenodo.9540.

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29

Earls, Jason. "SMARANDACHE REPLICATING DIGITAL FUNCTION NUMBERS." August 22, 2006. https://doi.org/10.5281/zenodo.9564.

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In 1987, Mike Keith introduced "repfigits" (replicating Fibonacci-like digits) [1]. In this paper two generalizations of repfigits are presented in which Smarandache type functions are applied to the digits of n. Some conjectures and unsolved questions are then proposed.

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30

IACOBESCU, Fanel. "SMARANDACHE PARTITION TYPE AND OTHER SEQUENCES." May 1, 1997. https://doi.org/10.5281/zenodo.9474.

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31

Smith, Sylvester. "A SET OF CONJECTURES ON SMARANDACHE SEQUENCES." September 14, 2001. https://doi.org/10.5281/zenodo.9626.

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Searching through the Archives of the Arizona State University, I found interesting sequences of numbers and problems related to them. I display some of them, and the readers are welcome to contribute with solutions or ideas.

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32

Maohua, Le. "TWO CONJECTURES CONCERNING EXTENTS OF SMARANDACHE FACTOR PARTITIONS." August 15, 2001. https://doi.org/10.5281/zenodo.9048.

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33

Karama, Muneer Jebreel. "Perfect powers in Smarandache n-Expressions." July 6, 2006. https://doi.org/10.5281/zenodo.9463.

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Is studied the concept of Smarandache n-expressions, for example I proposed formulas, found solutions, proposed open questions, and conjectured, but all for the fixed 3, and 2 numbers, but what will happen if these equations have diferent fixed numbers such as 7? This paper will answer this question.

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34

Gouveia, Paulo D. F., and Delfim F.M. Torres. "Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System." November 4, 2001. https://doi.org/10.5281/zenodo.9476.

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35

Russo, Felice. "An introduction to the Smarandache Double factorial function." June 24, 2000. https://doi.org/10.5281/zenodo.9186.

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36

Paulo, D. F. Gouveia, and F. M. Torres Delfim. "Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System." November 29, 2003. https://doi.org/10.5281/zenodo.32343.

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37

Gouveia, Paulo, and Delfim Torres. "Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System." June 1, 2000. https://doi.org/10.5281/zenodo.9215.

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38

Coman, Marius. "The Smarandache-Coman function and nine conjectures on it." August 6, 2010. https://doi.org/10.5281/zenodo.23252.

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The Smarandache-Coman function is the function defined on the set of non-null positive integers with values in the set of non-null positive integers in the following way: SC(n) is the least number such that SC(n)! is divisible by n + r, where r is the digital root of the number n. In other words, SC(n) = S(n + r), where S is the Smarandache function. I also state, in this paper, nine conjectures on this function which seems to be particularly interesting: beside other characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the n

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39

Yani, Zheng. "On the Pseudo Smarandache function and its two conjectures." November 9, 2007. https://doi.org/10.5281/zenodo.9096.

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The main purpose of this paper is using the elementary method to study the properties of the Pseudo-Smarandache function Z(n), and solve two conjectures posed by Kenichiro Kashihara in reference.

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40

Hasan, Sankari, and Abobala Mohammad. "Solving Three Conjectures about Neutrosophic Quadruple Vector Spaces." December 1, 2020. https://doi.org/10.5281/zenodo.4300602.

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aim of this paper is to answer Smarandache conjectures about neutrosophic quadruple vector spaces. This paper depends on the concept of weak n-refined neutrosophic vector space to prove that an NQ vector space V defined over the field F

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41

Murthy, A. "EXPLORING SOME NEW IDEAS ON SMARANDACHE TYPE SETS, FUNCTIONS AND SEQUENCES." February 1, 1996. https://doi.org/10.5281/zenodo.8984.

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In this article I have defined a number of SMARANDACHE type sets ,sequences which I found very interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this field.

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42

Balaji, V. "Solution of a Conjecture on Skolem Mean Graph." March 1, 2011. https://doi.org/10.5281/zenodo.9495.

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43

Sebastián, Martín Ruiz, and Perez Minh. "Propiedades y Problemas relacionados con las Funciones de Smarandache." December 13, 2002. https://doi.org/10.5281/zenodo.1042000.

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In this paper we present the definitions and some properties of several Smarandache type functions that are involved in many proposed solved and unsolved problems and conjectures in number theory and recreational mathematics. Examples are also provided. Interesting problems related to them are proposed as addenda to this article.

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44

Yahui, Yuy, and Caiz Lixiang. "On the Smarandache prime part sequences and its two conjectures1." August 7, 2008. https://doi.org/10.5281/zenodo.9488.

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45

Li, Xiaoxue, and Di Han. "On the Smarandache-Pascal derived sequences and some of their conjectures." Advances in Difference Equations 2013, no. 1 (2013). http://dx.doi.org/10.1186/1687-1847-2013-240.

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