Volume 3, Issue 2, June 2018, Page: 32-35
An Binary Problem of Goldbach Euler and Its Generalization
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
Received: Mar. 30, 2018;       Accepted: May 3, 2018;       Published: May 24, 2018
DOI: 10.11648/j.dmath.20180302.11      View  1726      Downloads  138
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.
Prime Numbers, Binary Problem, Axiom of Descent
To cite this article
Bagram Sibgatullovich Kochkarev, An Binary Problem of Goldbach Euler and Its Generalization, International Journal of Discrete Mathematics. Vol. 3, No. 2, 2018, pp. 32-35. doi: 10.11648/j.dmath.20180302.11
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Vinogradov I. M. Represantation of an odd number as a sum of three primes. Dokl. Akad. Nauk. SSR 15 (1937). 291-294.
Helfgott. La conjectura debil de Goldbach. Gac. R. Soc. Mat. Esp. 16 (2013) no 4.
Kochkarev B. S. K metody spuska Ferma. Problems of modern science and education. No 11 (41) (2015). 7-10. (in Russian).
Kochkarev B. S. Problema bliznetsov I drugie binarnye problemy. Problems of modern science and education. No 11 (41) (2015). 10-12. (in Russian)
Bukhshtab A. A. Teoriya Chisel. Izd. “Prosvetchenie”, Moskva. 1966. 384s.
Singh S. Velikaya teorema Ferma.-M.: Izd. Moskovskogo Tsentra nepreryvnogo obrazovaniya, 2000. 288 s. (in Russian).
Kochkarev B. S. Algorithm of Search of Large Prime Numbers, International Journal of Discrete Mathematics, Jan. 17, 2017, 30-32.
Postnikov M. M. Vvedenie v teoriyu algebraicheskikh chisel. Moskva, “nauka” Glavnaya redktsiya fiziko-matematicheskoy literatury, 1982, s. 240 (in Russian).
Kochkarev B. S. Axiom of Descent and Binary Mathematical Problems, American of Engineering Research (AJER) Volume-7, Issue-2 pp. 117-118.
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.
Laptev B. L. Nikolai Ivanovich Lobachevsky izd. Kazanskogo Universiteta. 1976. 136 s.
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.
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.
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/...
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.
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).
Matiyasevich Yu. V. Diophantine sets, Uspekhi Matematicheskikh Nauk, 27:5 (167) (1972), 185-222 (NN Russian)
Igoshin V. I. Matematicheskaya logika I teoriya algoritmov. Moskva, Academia, 2004, s. 448.
Browse journals by subject