An Binary Problem of Goldbach Euler and Its Generalization

Bagram Sibgatullovich Kochkarev

doi:doi:10.11648/j.dmath.20180302.11

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An Binary Problem of Goldbach Euler and Its Generalization

Bagram Sibgatullovich Kochkarev

Published in International Journal of Discrete Mathematics (Volume 3, Issue 2)

Received: 30 March 2018 Accepted: 3 May 2018 Published: 24 May 2018

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Abstract

We prove that for any even positive integer 2k greater than 6 one can find a pair of primes one of which is less than k and the other is greater than k and their sum is 2k. The article shows that such property of even numbers allows to build effective cryptographic systems.

Published in	International Journal of Discrete Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.dmath.20180302.11
Page(s)	32-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Prime Numbers, Binary Problem, Axiom of Descent

References

[1]	Vinogradov I. M. Represantation of an odd number as a sum of three primes. Dokl. Akad. Nauk. SSR 15 (1937). 291-294.
[2]	Helfgott. La conjectura debil de Goldbach. Gac. R. Soc. Mat. Esp. 16 (2013) no 4.
[3]	Kochkarev B. S. K metody spuska Ferma. Problems of modern science and education. No 11 (41) (2015). 7-10. (in Russian).
[4]	Kochkarev B. S. Problema bliznetsov I drugie binarnye problemy. Problems of modern science and education. No 11 (41) (2015). 10-12. (in Russian)
[5]	Bukhshtab A. A. Teoriya Chisel. Izd. “Prosvetchenie”, Moskva. 1966. 384s.
[6]	Singh S. Velikaya teorema Ferma.-M.: Izd. Moskovskogo Tsentra nepreryvnogo obrazovaniya, 2000. 288 s. (in Russian).
[7]	Kochkarev B. S. Algorithm of Search of Large Prime Numbers, International Journal of Discrete Mathematics, Jan. 17, 2017, 30-32.
[8]	Postnikov M. M. Vvedenie v teoriyu algebraicheskikh chisel. Moskva, “nauka” Glavnaya redktsiya fiziko-matematicheskoy literatury, 1982, s. 240 (in Russian).
[9]	Kochkarev B. S. Axiom of Descent and Binary Mathematical Problems, American of Engineering Research (AJER) Volume-7, Issue-2 pp. 117-118.
[10]	Kochkarev B. S. Infinite Sequences Primes of Form 4n-1 and 4n+1, International Journal of Humanities and Social Science Invention, Vol. 5, Issue, 12. December, 2016, pp. 102-108.
[11]	Laptev B. L. Nikolai Ivanovich Lobachevsky izd. Kazanskogo Universiteta. 1976. 136 s.
[12]	Wiles A. Modular elliptic curves and Fermat’s last theorem. Annals of Mathematics. V. 141 Second series 3 May 1995 pp. 445-551. International Journal of Disctete Mathematics, Jan. 17, 2017, 30-32.
[13]	Kochkarev B. S. About One Binary Problem in a Class of Algebraic Equations and Her Communication with the Great Hypothesis of Fermat. International Journal of Current Multidisciplinary Studies, Vol. 2, Issue, 10, pp. 457-459, October, 2016.
[14]	Kochkarev B. S. About One Binary Problem in a Certain Class of Algebraic Equations and its Connection with the Great Hypothesis Farm, https://dspace.kpfu.ru/xmlui/bi9tstream/handle/net/...
[15]	Kochkarev B. S. About Tenth Problem of D. Hilbert, American Journal of Engineering Research (AJER), 2017, Vol. 6, Issue, 12, pp. 241-242 www.ajer. Org Open Access.
[16]	Kochkarev B. S. Ob odnom algoritme, ne soglasuyutchemsya s tezisami Turinga, Chercha I Markova, Problems of modern Science and Education, 2014, 3 (21)23-25 (in Russian).
[17]	Matiyasevich Yu. V. Diophantine sets, Uspekhi Matematicheskikh Nauk, 27:5 (167) (1972), 185-222 (NN Russian)
[18]	Igoshin V. I. Matematicheskaya logika I teoriya algoritmov. Moskva, Academia, 2004, s. 448.

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Bagram Sibgatullovich Kochkarev. (2018). An Binary Problem of Goldbach Euler and Its Generalization. International Journal of Discrete Mathematics, 3(2), 32-35. https://doi.org/10.11648/j.dmath.20180302.11

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ACS Style

Bagram Sibgatullovich Kochkarev. An Binary Problem of Goldbach Euler and Its Generalization. Int. J. Discrete Math. 2018, 3(2), 32-35. doi: 10.11648/j.dmath.20180302.11

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AMA Style

Bagram Sibgatullovich Kochkarev. An Binary Problem of Goldbach Euler and Its Generalization. Int J Discrete Math. 2018;3(2):32-35. doi: 10.11648/j.dmath.20180302.11

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@article{10.11648/j.dmath.20180302.11,
  author = {Bagram Sibgatullovich Kochkarev},
  title = {An Binary Problem of Goldbach Euler and Its Generalization},
  journal = {International Journal of Discrete Mathematics},
  volume = {3},
  number = {2},
  pages = {32-35},
  doi = {10.11648/j.dmath.20180302.11},
  url = {https://doi.org/10.11648/j.dmath.20180302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20180302.11},
  abstract = {We prove that for any even positive integer 2k greater than 6 one can find a pair of primes one of which is less than k and the other is greater than k and their sum is 2k. The article shows that such property of even numbers allows to build effective cryptographic systems.},
 year = {2018}
}

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TY  - JOUR
T1  - An Binary Problem of Goldbach Euler and Its Generalization
AU  - Bagram Sibgatullovich Kochkarev
Y1  - 2018/05/24
PY  - 2018
N1  - https://doi.org/10.11648/j.dmath.20180302.11
DO  - 10.11648/j.dmath.20180302.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 32
EP  - 35
PB  - Science Publishing Group
SN  - 2578-9252
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AB  - We prove that for any even positive integer 2k greater than 6 one can find a pair of primes one of which is less than k and the other is greater than k and their sum is 2k. The article shows that such property of even numbers allows to build effective cryptographic systems.
VL  - 3
IS  - 2
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Author Information

Bagram Sibgatullovich Kochkarev

Department of Mathematics and Mathematical Modeling, Institute of Mathematics and Mechanics Named After Nikolai Ivanovich Lobachevsky, Kazan (Volga Region) Federal University, Kazan, Russia

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APA Style

Bagram Sibgatullovich Kochkarev. (2018). An Binary Problem of Goldbach Euler and Its Generalization. International Journal of Discrete Mathematics, 3(2), 32-35. https://doi.org/10.11648/j.dmath.20180302.11

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ACS Style

Bagram Sibgatullovich Kochkarev. An Binary Problem of Goldbach Euler and Its Generalization. Int. J. Discrete Math. 2018, 3(2), 32-35. doi: 10.11648/j.dmath.20180302.11

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AMA Style

Bagram Sibgatullovich Kochkarev. An Binary Problem of Goldbach Euler and Its Generalization. Int J Discrete Math. 2018;3(2):32-35. doi: 10.11648/j.dmath.20180302.11

Copy | Download

@article{10.11648/j.dmath.20180302.11,
  author = {Bagram Sibgatullovich Kochkarev},
  title = {An Binary Problem of Goldbach Euler and Its Generalization},
  journal = {International Journal of Discrete Mathematics},
  volume = {3},
  number = {2},
  pages = {32-35},
  doi = {10.11648/j.dmath.20180302.11},
  url = {https://doi.org/10.11648/j.dmath.20180302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20180302.11},
  abstract = {We prove that for any even positive integer 2k greater than 6 one can find a pair of primes one of which is less than k and the other is greater than k and their sum is 2k. The article shows that such property of even numbers allows to build effective cryptographic systems.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - An Binary Problem of Goldbach Euler and Its Generalization
AU  - Bagram Sibgatullovich Kochkarev
Y1  - 2018/05/24
PY  - 2018
N1  - https://doi.org/10.11648/j.dmath.20180302.11
DO  - 10.11648/j.dmath.20180302.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 32
EP  - 35
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20180302.11
AB  - We prove that for any even positive integer 2k greater than 6 one can find a pair of primes one of which is less than k and the other is greater than k and their sum is 2k. The article shows that such property of even numbers allows to build effective cryptographic systems.
VL  - 3
IS  - 2
ER  -

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