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Journal articles on the topic 'Number theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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1

C.S., Harisha. "Graph Theory Approach to Number Theory Theorems." Journal of Advanced Research in Dynamical and Control Systems 12, no. 01-Special Issue (2020): 568–72. http://dx.doi.org/10.5373/jardcs/v12sp1/20201105.

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2

Lefevre, Adam. "Number Theory." Grand Street, no. 59 (1997): 99. http://dx.doi.org/10.2307/25008125.

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3

Scourfield, E. J. "NUMBER THEORY." Bulletin of the London Mathematical Society 17, no. 1 (1985): 93–94. http://dx.doi.org/10.1112/blms/17.1.93.

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4

Schroeder, M. R. "Number theory." IEEE Potentials 8, no. 3 (1989): 14–17. http://dx.doi.org/10.1109/45.41531.

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5

Balasubramanian, K. "Number Theory." Journal of Mathematical Chemistry 36, no. 2 (2004): 167. http://dx.doi.org/10.1023/b:jomc.0000038791.72217.20.

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6

Wang, Mingshen. "Group Theory in Number Theory." Theoretical and Natural Science 5, no. 1 (2023): 9–13. http://dx.doi.org/10.54254/2753-8818/5/20230254.

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The theory of groups exists in many fields of mathematics and has made a great impact on many fields of mathematics. In this article, this paper first introduces the history of group theory and elementary number theory, and then lists the definitions of group, ring, field and the most basic prime and integer and divisor in number theory that need to be used in this article. Then from the definitions, step by step, Euler's theorem, Bzout's lemma, Wilson's theorem and Fermat's Little theorem in elementary number theory are proved by means of definitions of group theory, cyclic groups, and even polynomials over domains. Finally, some concluding remarks are made. Many number theory theorems can be proved directly by the method of group theory without the action of tricks in number theory. Number theory is the thinking of certain special groups (e.g., (Z,+),(Z,)), so the methods of group theory work well inside number theory.

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7

Grosswald, Emil, Charles Vanden Eynden, and Kenneth H. Rosen. "Elementary Number Theory." American Mathematical Monthly 96, no. 5 (1989): 460. http://dx.doi.org/10.2307/2325169.

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8

Blackmore, G. W., I. N. Stewart, and D. O. Tall. "Algebraic Number Theory." Mathematical Gazette 73, no. 463 (1989): 65. http://dx.doi.org/10.2307/3618234.

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9

Bowen, Alan C. "Boethian Number Theory." Ancient Philosophy 9, no. 1 (1989): 137–43. http://dx.doi.org/10.5840/ancientphil19899136.

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10

Shiu, P., Gareth A. Jones, and J. Mary Jones. "Elementary Number Theory." Mathematical Gazette 82, no. 495 (1998): 534. http://dx.doi.org/10.2307/3619931.

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11

Brüdern, Jörg, Hugh Montgomery, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 10, no. 4 (2013): 2963–3037. http://dx.doi.org/10.4171/owr/2013/51.

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12

Brüdern, Jörg, Hugh Montgomery, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 13, no. 4 (2017): 2975–3030. http://dx.doi.org/10.4171/owr/2016/53.

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13

Brüdern, Jörg, Kaisa Matomäki, Robert Vaughan, and Trevor Wooley. "Analytic Number Theory." Oberwolfach Reports 16, no. 4 (2020): 3141–205. http://dx.doi.org/10.4171/owr/2019/50.

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14

Snapp, Bart, and Chris Snapp. "Automotive Number Theory." Math Horizons 17, no. 1 (2009): 26–27. http://dx.doi.org/10.1080/10724117.2009.11974839.

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15

Tokuo, Kenji. "Quantum Number Theory." International Journal of Theoretical Physics 43, no. 12 (2004): 2461–81. http://dx.doi.org/10.1007/s10773-004-7711-6.

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16

Iwaniec, Henryk. "Automorphic Number Theory." Current Developments in Mathematics 2003, no. 1 (2003): 35–52. http://dx.doi.org/10.4310/cdm.2003.v2003.n1.a2.

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17

Snapp, Bart, and Chris Snapp. "Automotive Number Theory." Math Horizons 17, no. 1 (2009): 26–27. http://dx.doi.org/10.4169/194762109x468328.

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18

Matomäki, Kaisa, Kannan Soundararajan, Robert C. Vaughan, and Trevor D. Wooley. "Analytic Number Theory." Oberwolfach Reports 19, no. 4 (2023): 2895–960. http://dx.doi.org/10.4171/owr/2022/50.

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19

Peleshenko, Vitaly A. "QUANTUMCOMPUTATIONAL NUMBER THEORY." SOFT MEASUREMENTS AND COMPUTING 12, no. 61 (2022): 32–51. http://dx.doi.org/10.36871/2618-9976.2022.12.003.

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The article is devoted to the issues of quantum computational number theory. The prerequisites that gave impetus to its formation, as well as the main provisions regulating its further development, are revealed.

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20

Siagian, Pargaulan, Waminton Rajagukguk, and Faiz Ahyaningsih. "Development of Problem-Based Number Theory Learning Tools." PARADIKMA: JURNAL PENDIDIKAN MATEMATIKA 16, no. 1 (2023): 52–56. http://dx.doi.org/10.24114/paradikma.v16i1.42074.

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Development of Problem-Based Number Theory Learning Tools" in the 2022 FMIPA Unimed Mathematics Education Lecture. This research is the development of learning tools that aim to describe the development process that produces valid, practical, and effective number theory learning tools. Problem-Based Number Theory Learning developed by following the Four D's: Define, Design, Develop, and Disseminate. The trial of device development was carried out in the S1 Mathematics Education Study program in the Number Theory lecture. In the development of number theory lecture tools produce: Textbooks, and 14 Lesson Plans (LP) that are valid, practical and effective. The implementation process is carried out by preparing components of teaching materials for the Number Theory course in the form of: textbooks, LP which are carried out in the Number Theory course in 2022. In the implementation of disseminate applying limited Number Theory teaching materials produced: LP as many as 14 valid, practical and effective meetings to the Lecturer Team in the Department of Mathematics FMIPA Unimed

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21

Maslov, V. P. "Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics." Russian Journal of Mathematical Physics 23, no. 4 (2016): 510–28. http://dx.doi.org/10.1134/s1061920816040075.

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22

Rajasekaran, Aayush, Jeffrey Shallit, and Tim Smith. "Additive Number Theory via Automata Theory." Theory of Computing Systems 64, no. 3 (2019): 542–67. http://dx.doi.org/10.1007/s00224-019-09929-9.

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23

Quadling, Douglas, Bob Burn, and Amanda Chetwynd. "A Cascade of Numbers: An Introduction to Number Theory." Mathematical Gazette 81, no. 491 (1997): 329. http://dx.doi.org/10.2307/3619238.

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24

Shiu, P., and Paulo Ribenboim. "My Numbers, My Friends. Popular Lectures on Number Theory." Mathematical Gazette 85, no. 504 (2001): 540. http://dx.doi.org/10.2307/3621797.

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25

Marshall, John U. "The Löschian Numbers As a Problem in Number Theory." Geographical Analysis 7, no. 4 (2010): 421–26. http://dx.doi.org/10.1111/j.1538-4632.1975.tb01054.x.

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26

Gode, Deepak Bhalchandra. "Complex Number Theory without Imaginary Number (i)." OALib 01, no. 07 (2014): 1–13. http://dx.doi.org/10.4236/oalib.1100856.

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27

Steele, G. Ander. "Carmichael numbers in number rings." Journal of Number Theory 128, no. 4 (2008): 910–17. http://dx.doi.org/10.1016/j.jnt.2007.08.009.

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28

Berndt, Bruce C., and D. P. Parent. "Exercises in Number Theory." American Mathematical Monthly 93, no. 8 (1986): 667. http://dx.doi.org/10.2307/2322349.

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29

Beigel, Richard. "Irrationality Without Number Theory." American Mathematical Monthly 98, no. 4 (1991): 332. http://dx.doi.org/10.2307/2323801.

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30

Mazur, B. "Number Theory as Gadfly." American Mathematical Monthly 98, no. 7 (1991): 593. http://dx.doi.org/10.2307/2324924.

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31

Jackson, Terence, Adolf Hurwitz, Nikolaos Kritikos, and W. C. Schulz. "Lectures on Number Theory." Mathematical Gazette 71, no. 457 (1987): 246. http://dx.doi.org/10.2307/3616787.

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32

Slomson, Alan, and Craig Smorynski. "Logical Number Theory I." Mathematical Gazette 76, no. 477 (1992): 421. http://dx.doi.org/10.2307/3618411.

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33

Shiu, P., and Don Redman. "Number Theory: An Introduction." Mathematical Gazette 81, no. 490 (1997): 165. http://dx.doi.org/10.2307/3618815.

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34

Shiu, P., and A. A. Karatsuba. "Basic Analytic Number Theory." Mathematical Gazette 79, no. 484 (1995): 213. http://dx.doi.org/10.2307/3620091.

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35

Shiu, P. "Progress in Number Theory." Mathematical Gazette 80, no. 487 (1996): 54. http://dx.doi.org/10.2307/3620332.

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36

Pargeter, A. Robert, and Song Y. Yan. "Number Theory for Computing." Mathematical Gazette 84, no. 501 (2000): 553. http://dx.doi.org/10.2307/3620808.

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37

Shiu, P., and George Greaves. "Sieves in Number Theory." Mathematical Gazette 86, no. 507 (2002): 550. http://dx.doi.org/10.2307/3621188.

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38

S., R., and Michael E. Pohst. "Computational Algebraic Number Theory." Mathematics of Computation 64, no. 212 (1995): 1763. http://dx.doi.org/10.2307/2153389.

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39

Parsonson, S. L., and I. M. Hall. "Topics in Number Theory." Mathematical Gazette 70, no. 451 (1986): 61. http://dx.doi.org/10.2307/3615846.

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40

Karatsuba, A. A. "Euler and number theory." Proceedings of the Steklov Institute of Mathematics 264, no. 1 (2009): 74–86. http://dx.doi.org/10.1134/s0081543809010106.

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41

Karatsuba, A. A. "Euler and number theory." Proceedings of the Steklov Institute of Mathematics 274, S1 (2011): 169–79. http://dx.doi.org/10.1134/s0081543811070042.

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42

Dence, Thomas P., and Jenise A. Smalley. "Number Theory Crossword Puzzle." Math Horizons 14, no. 2 (2006): 22–23. http://dx.doi.org/10.1080/10724117.2006.11974677.

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43

Schumer, Peter. "Biscuits of Number Theory." Math Horizons 17, no. 2 (2009): 29. http://dx.doi.org/10.1080/10724117.2009.11974853.

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44

Nakayama, Kazunori, Fuminobu Takahashi, and Tsutomu T. Yanagida. "Number-theory dark matter." Physics Letters B 699, no. 5 (2011): 360–63. http://dx.doi.org/10.1016/j.physletb.2011.04.035.

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45

Ram Murty, M. "Littlewood and number theory." Resonance 18, no. 9 (2013): 789–98. http://dx.doi.org/10.1007/s12045-013-0103-6.

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46

Mazur, B. "Number Theory as Gadfly." American Mathematical Monthly 98, no. 7 (1991): 593–610. http://dx.doi.org/10.1080/00029890.1991.11995762.

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47

Beigel, Richard. "Irrationality Without Number Theory." American Mathematical Monthly 98, no. 4 (1991): 332–35. http://dx.doi.org/10.1080/00029890.1991.12000762.

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48

Green, Frederic. "Review of Number Theory." ACM SIGACT News 50, no. 1 (2019): 9–13. http://dx.doi.org/10.1145/3319627.3319630.

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49

Hadas, Ofer, Anne Henke та Amitai Regev. "ℤ2-Graded Number Theory". Communications in Algebra 34, № 8 (2006): 3077–95. http://dx.doi.org/10.1080/00927870600640086.

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50

Gorgui-Naguib, R. N. "p-adic number theory." IEE Proceedings G (Electronic Circuits and Systems) 135, no. 3 (1988): 107. http://dx.doi.org/10.1049/ip-g-1.1988.0016.

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