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Journal articles on the topic 'Two Numbers'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Adédji, Kouèssi Norbert, Japhet Odjoumani, and Alain Togbé. "Padovan and Perrin numbers as products of two generalized Lucas numbers." Archivum Mathematicum, no. 4 (2023): 315–37. http://dx.doi.org/10.5817/am2023-4-315.

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2

Finney, David J. "On Comparing Two Numbers." Teaching Statistics 29, no. 1 (2007): 17–20. http://dx.doi.org/10.1111/j.1467-9639.2007.00251.x.

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3

Shen, Jian. "On two Turán Numbers." Journal of Graph Theory 51, no. 3 (2006): 244–50. http://dx.doi.org/10.1002/jgt.20141.

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4

BuxDPI, BNYuldashev. "PROBLEMS OF FINDING THESE NUMBERS ACCORDING TO THE SUM (OR DIFFERENCE) AND MULTIPLE RATIO OF TWO NUMBERS." European International Journal of Pedagogics 4, no. 12 (2024): 65–70. https://doi.org/10.55640/eijp-04-12-13.

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5

Xu, Aimin. "Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers." Results in Mathematics 72, no. 4 (2017): 1857–64. http://dx.doi.org/10.1007/s00025-017-0748-7.

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6

Honwei, Shi, Mi Zhou, Zhang Delong, Jiang Xingyi, and He Songting. "Even numbers are the sum of two prime numbers." Greener Journal of Science, Engineering and Technological Research 9, no. 1 (2019): 8–11. http://dx.doi.org/10.15580/gjsetr.2019.1.040919068.

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7

Luca, Florian, Japhet Odjoumani, and Alain Togbé. "Tribonacci Numbers That Are Products of Two Fibonacci Numbers." Fibonacci Quarterly 61, no. 4 (2023): 298–304. http://dx.doi.org/10.1080/00150517.2023.12427384.

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8

Ddamulira, Mahadi, Florian Luca, and Mihaja Rakotomalala. "Fibonacci Numbers which are Products of two Pell Numbers." Fibonacci Quarterly 54, no. 1 (2016): 11–18. http://dx.doi.org/10.1080/00150517.2016.12427833.

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9

Murat, Alan. "Mersenne numbers as a difference of two Lucas numbers." Commentationes Mathematicae Universitatis Carolinae 63, no. 3 (2023): 269–76. http://dx.doi.org/10.14712/1213-7243.2022.027.

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10

Honwei, Shi, Mi Zhou, Zhang Delong, Jiang Xingyi, and He Songting. "Even numbers are the sum of two prime numbers." Greener Journal of Science, Engineering and Technological Research 9, no. 1 (2019): 8–11. https://doi.org/10.15580/GJSETR.2019.1.040919068.

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<strong>"Even numbers are the sum of two prime numbers." This is the description of Goldbach's conjecture, and in Canadian Gaye's book "unsolved problems in number theory", it is an open question to put forward a contrary conjecture that "even numbers are the difference between two prime numbers". In this paper, Chandra sieve is used to deduce that the sum of large and even numbers is the sum of two prime numbers, and that "even numbers are the difference between two prime numbers" is a great possibility. At the same time, it is possible to guess

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11

Daşdemir, Ahmet, and Mehmet Varol. "Lucas Numbers Which Are Products of Two Pell Numbers." Fibonacci Quarterly 63, no. 1 (2025): 78–83. https://doi.org/10.1080/00150517.2024.2412958.

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12

Barghi, Mohammadreza. "A New Conjecture: Any Whole Number Greater than 3 has the Equal Distance from Two Prime Numbers." International Journal of Science and Research (IJSR) 12, no. 10 (2023): 540–41. http://dx.doi.org/10.21275/sr231006065849.

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13

Tho, Nguyen Xuan. "Two theorems on square numbers." Notes on Number Theory and Discrete Mathematics 28, no. 1 (2022): 75–80. http://dx.doi.org/10.7546/nntdm.2022.28.1.75-80.

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We show that if a is a positive integer such that for each positive integer n, a+n^2 can be expressed x^2+y^2, where x,y\in \mathbb{Z}, then a is a square number. A similar theorem also holds if a+n^2 and x^2+y^2 are replaced by a+2n^2 and x^2+2y^2, respectively.

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14

Ganor-Stern, Dana, Joseph Tzelgov, and Ravid Ellenbogen. "Automaticity and two-digit numbers." Journal of Experimental Psychology: Human Perception and Performance 33, no. 2 (2007): 483–96. http://dx.doi.org/10.1037/0096-1523.33.2.483.

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15

Griggs, Jerrold R. "Iterated exponentials of two numbers." Discrete Mathematics 88, no. 2-3 (1991): 193–209. http://dx.doi.org/10.1016/0012-365x(91)90009-q.

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16

Shparlinski, Igor E., and Arne Winterhof. "Partitions into two Lehmer numbers." Monatshefte für Mathematik 160, no. 4 (2009): 429–41. http://dx.doi.org/10.1007/s00605-009-0130-2.

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17

Burgos, Albert. "Two results about Matula numbers." Discrete Mathematics 323 (May 2014): 58–62. http://dx.doi.org/10.1016/j.disc.2014.01.009.

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18

Sofo, Anthony. "Harmonic numbers of order two." Miskolc Mathematical Notes 13, no. 2 (2012): 499. http://dx.doi.org/10.18514/mmn.2012.430.

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19

Drmota, Michael, Christian Mauduit, and Joël Rivat. "Prime numbers in two bases." Duke Mathematical Journal 169, no. 10 (2020): 1809–76. http://dx.doi.org/10.1215/00127094-2019-0083.

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20

Bhattacharya, Soumya. "Sum of Two Triangular Numbers." Resonance 29, no. 6 (2024): 857–61. http://dx.doi.org/10.1007/s12045-024-0857-z.

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21

Verguts, Tom, and Wendy De Moor. "Two-digit Comparison." Experimental Psychology 52, no. 3 (2005): 195–200. http://dx.doi.org/10.1027/1618-3169.52.3.195.

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Abstract. We investigate whether two-digit numbers are decomposed for purposes of numerical comparison (e.g., choosing the larger one). Earlier theorists concluded that numbers are processed holistically ( Brysbaert, 1995 ; Dehaene, Dupoux, & Mehler, 1990 ), or that holistic and decomposed processes operate in parallel ( Nuerk, Weger, & Willmes, 2001 ). In the present experiment, we presented pairs of two-digit numbers with a decade distance of either zero (e.g., 54-57) or one (54-61). If a holistic process contributes to two-digit comparison, there should be an overall distance effect

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22

Fitousi, Daniel, and Daniel Algom. "Size congruity effects with two-digit numbers: Expanding the number line?" Memory & Cognition 34, no. 2 (2006): 445–57. http://dx.doi.org/10.3758/bf03193421.

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23

Ewell, John A. "On Representations of Numbers by Sums of Two Triangular Numbers." Fibonacci Quarterly 30, no. 2 (1992): 175–78. http://dx.doi.org/10.1080/00150517.1992.12429374.

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24

Griffiths, Martin, and Alex Bramham. "The Jacobsthal Numbers: two Results and two Questions." Fibonacci Quarterly 53, no. 2 (2015): 147–51. http://dx.doi.org/10.1080/00150517.2015.12428277.

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25

Zhou, Mi, and Yuan Guo. "New Solutions to Solve Two Conjectures." Greener Journal of Science, Engineering and Technological Research 7, no. 2 (2017): 21–24. https://doi.org/10.15580/GJSETR.2017.2.052117066.

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Based on digital black hole findings, this paper provided a new method for investigating the twin prime number issue. That is, writing down the prime numbers in sequence, counting the number of the prime numbers, the number of the twin prime numbers and the sum of these two numbers from the given numeric string respectively. After iteration repeatedly, the finally result will certainly fall into the black hole of either 000 or 202, testifying that there are infinite numbers of twin prime numbers. This new special method deals with the problem of twin prime numbers easily and effectively with p

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26

Lycan, Ron, and Vadim Ponomarenko. "Sums of Two Generalized Tetrahedral Numbers." PUMP Journal of Undergraduate Research 5 (December 23, 2022): 206–17. http://dx.doi.org/10.46787/pump.v5i0.3329.

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Expressing whole numbers as sums of figurate numbers, including tetrahedral numbers, is a longstanding problem in number theory. Pollock's tetrahedral number conjecture states that every positive integer can be expressed as the sum of at most five tetrahedral numbers. Here we explore a generalization of this conjecture to negative indices. We provide a method for computing sums of two generalized tetrahedral numbers up to a given bound, and explore which families of perfect powers can be expressed as sums of two generalized tetrahedral numbers.

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27

KÖKEN, Fikri, and Emre KANKAL. "Altered Numbers of Fibonacci Number Squared." Journal of New Theory, no. 45 (December 31, 2023): 73–82. http://dx.doi.org/10.53570/jnt.1368751.

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We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$. These numbers are significant as they are related to the consecutive products of the Fibonacci numbers. As a result, we establish consecutive sum-subtraction relations of altered Fibonacci numbers and their Binet-like formulas. Moreover, we explore greatest common divisor (GCD) sequences of r-successive terms of altered Fibonacci numbers represented by $\left\{G^{(2)}_{F(n), r}(a)\right\}$

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28

Egge, Eric S., and Toufik Mansour. "132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers." Discrete Applied Mathematics 143, no. 1-3 (2004): 72–83. http://dx.doi.org/10.1016/j.dam.2003.12.007.

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29

Gaber, Ahmed, and Mohiedeen Ahmed. "Coincidence of modified Pell numbers and sums of two Jacobsthal numbers." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 1 (2025): 205–16. https://doi.org/10.47974/jdmsc-2138.

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Let {qr}r ≥ 0 and {Jr}r ≥ 0 denote Modified Pell and Jacobsthal numbers sequences, respectively. We solve the equation qr = Js + Jt using Matveev’s fundamental variant of Baker’s linear forms theory. Then a reduction procedure of Dujella and Pethö is employed to bring the obtained bounds to a relatively more investigatable domain.

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30

Shulga, Nikita. "Rational approximations to two irrational numbers." Moscow Journal of Combinatorics and Number Theory 11, no. 1 (2022): 1–10. http://dx.doi.org/10.2140/moscow.2022.11.1.

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31

García-Orza, Javier, and Jesús Damas. "Sequential Processing of Two-Digit Numbers." Zeitschrift für Psychologie 219, no. 1 (2011): 23–29. http://dx.doi.org/10.1027/2151-2604/a000042.

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Two experiments using a number matching task (NMT) explored whether two-digit numbers are processed holistically or in a compositional fashion. In the NMT participants are required to decide whether one of the two numbers initially provided (cues) is presented some milliseconds later or not (probe). Probes which have some arithmetic relationship to the cues (e.g., cues: 2 3, probe: 6) are rejected more slowy than probes unrelated to their cues (e.g., cues: 2 3, probe: 7) – interference effect –, and this is considered as evidence of the automatic activation of that arithmetic relationship. Par

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32

Byun, Jisoo, and Yong Sik Yun. "PARAMETRIC OPERATIONS FOR TWO FUZZY NUMBERS." Communications of the Korean Mathematical Society 28, no. 3 (2013): 635–42. http://dx.doi.org/10.4134/ckms.2013.28.3.635.

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33

Broere, Izak, and Marietjie Frick. "TWO RESULTS ON GENERALIZED CHROMATIC NUMBERS." Quaestiones Mathematicae 13, no. 2 (1990): 183–90. http://dx.doi.org/10.1080/16073606.1990.9631611.

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34

Rath, Purusottam. "Two exceptional classes of real numbers." Functiones et Approximatio Commentarii Mathematici 38, no. 1 (2008): 81–91. http://dx.doi.org/10.7169/facm/1229624653.

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35

Granville, Andrew, and Carl Pomerance. "Two contradictory conjectures concerning Carmichael numbers." Mathematics of Computation 71, no. 238 (2001): 883–909. http://dx.doi.org/10.1090/s0025-5718-01-01355-2.

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36

Baker, R. C., and J. Brüdern. "On sums of two squarefull numbers." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 1 (1994): 1–5. http://dx.doi.org/10.1017/s0305004100072340.

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A natural number n is said to be squarefull if p|n implies p2|n for primes p. The set of all squarefull numbers is not much more dense in the natural numbers than the set of perfect squares but their additive properties may be rather different. We are more precise only in the case of sums of two such integers as this is the problem with which we are concerned here. Let U(x) be the number of integers not exceeding x and representable as the sum of two integer squares. Then, according to a theorem of Landau [4],as x tends to infinity.

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37

Ramík, Jaroslav, and Kazuo Nakamura. "Canonical fuzzy numbers of dimension two." Fuzzy Sets and Systems 54, no. 2 (1993): 167–80. http://dx.doi.org/10.1016/0165-0114(93)90274-l.

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38

Abu-Saris, Raghib M., and Mowaffaq Hajja. "Geometric means of two positive numbers." Mathematical Inequalities & Applications, no. 3 (2006): 391–406. http://dx.doi.org/10.7153/mia-09-38.

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39

Zhang, Gengyu. "Crosscap Numbers of Two-component Links." Kyungpook mathematical journal 48, no. 2 (2008): 241–54. http://dx.doi.org/10.5666/kmj.2008.48.2.241.

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40

Zhuravleva, V. V. "On the two smallest Pisot numbers." Mathematical Notes 94, no. 5-6 (2013): 820–23. http://dx.doi.org/10.1134/s0001434613110163.

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41

Sun, Yidong. "Two classes of p-Stirling numbers." Discrete Mathematics 306, no. 21 (2006): 2801–5. http://dx.doi.org/10.1016/j.disc.2006.05.016.

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42

Holte, Robert, Louis Rosier, Igor Tulchinsky, and Donald Varvel. "Pinwheel scheduling with two distinct numbers." Theoretical Computer Science 100, no. 1 (1992): 105–35. http://dx.doi.org/10.1016/0304-3975(92)90365-m.

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43

Dempsey, Mike. "Polluted Rivers, Numbers One and Two." Critical Perspectives on Accounting 10, no. 1 (1999): 12. http://dx.doi.org/10.1006/cpac.1998.0330.

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44

Melfi, Giuseppe. "On Two Conjectures about Practical Numbers." Journal of Number Theory 56, no. 1 (1996): 205–10. http://dx.doi.org/10.1006/jnth.1996.0012.

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45

Uygun, Sukran. "Complex Jacobsthal Numbers in Two Dimension." Sarajevo Journal of Mathematics 20, no. 2 (2025): 219–29. https://doi.org/10.5644/sjm.20.02.04.

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In this paper, we present a new approach to the generalization of Jacobsthal sequences to the complex plane. It is shown that the Jacobsthal numbers are generalized to two dimensions. For special entries of this new sequence, some relations to the classical Jacobsthal sequences are constructed. Binet formula, the generating function, the explicit closed formula, the sum formula for the new two dimensional Gaussian Jacobsthal sequence are investigated. The relation with classical Jacobsthal Lucas numbers and two dimensional Gaussian Jacobsthal numbers are obtained by using Binet formula. From m

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46

Bar, Hofit, Martin H. Fischer, and Daniel Algom. "On the linear representation of numbers: evidence from a new two-numbers-to-two positions task." Psychological Research 83, no. 1 (2018): 48–63. http://dx.doi.org/10.1007/s00426-018-1063-y.

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47

HOECKNER, S., K. MOELLER, H. ZAUNER, et al. "Impairments of the mental number line for two-digit numbers in neglect." Cortex 44, no. 4 (2008): 429–38. http://dx.doi.org/10.1016/j.cortex.2007.09.001.

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48

Goddard, Cliff. "The conceptual semantics of numbers and counting." Functions of Language 16, no. 2 (2009): 193–224. http://dx.doi.org/10.1075/fol.16.2.02god.

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This study explores the conceptual semantics of numbers and counting, using the natural semantic metalanguage (NSM) technique of semantic analysis (Wierzbicka 1996; Goddard & Wierzbicka (eds.) 2002). It first argues that the concept of a number in one of its senses (number1, roughly, “number word”) and the meanings of low number words, such as one, two, and three, can be explicated directly in terms of semantic primes, without reference to any counting procedures or practices. It then argues, however, that the larger numbers, and the productivity of the number sequence, depend on the conce

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49

Bród, Dorota, Anetta Szynal-Liana, and Iwona Włoch. "Two Generalizations of Dual-Hyperbolic Balancing Numbers." Symmetry 12, no. 11 (2020): 1866. http://dx.doi.org/10.3390/sym12111866.

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In this paper, we study two generalizations of dual-hyperbolic balancing numbers: dual-hyperbolic Horadam numbers and dual-hyperbolic k-balancing numbers. We give Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity for them.

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50

Sass, Katharina, Lena Theissen, Thomas Munte, Ute Habel, and Arie Lugt. "The number decision task: Investigation of the representation of multi-digit numbers." Acta Neurobiologiae Experimentalis 73, no. 2 (2013): 289–303. http://dx.doi.org/10.55782/ane-2013-1937.

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The ability to process multi-digit numbers is an essential skill which we investigated using a number decision task. Subjects were asked to decide whether a target number (e.g., 649) is too small or too large to be the mean between two delimiter numbers that constituted the interval (e.g., 567 and 715). Three-digit numbers were presented vertically with (1) growing interval sizes (i.e., distance between the two delimiters; e.g., interval size between 567 and 715 is 148) and target gap to the mean (e.g., the gap between the ‘real’ mean 641 and the target 649 is 8) and (2) growing interval sizes

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