
Subsets of prime numbers in the generalized arithmetical progressions
The concept of the generalized arithmetical progression of the power k and difference d is given. For k 1,7 formulas of nth member of such progressions and for k 1, 2, 3 formulas for the sum of the first n its members are obtained. Progressions ( ) , k p d M with the first ...

What is Kantian Philosophy of Mathematics? An Overview of Contemporary Studies
... questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy ...

Analysis of Algorithms for Computing in Jacobian of a Picard Curve
... P. 13—28.
2. Sarlabous J. E., Barreirol E. R., Barceló J. A. P. On the Jacobian Varieties of Picard Curves: Explicit Addition Law and Algebraic Structure // Mathematische Nachrichten. 1999. № 208. P. 149—166.
3. Flon S., Oyono R. Fast Arithmetic on Jacobians of Picard Curves // Public Key Cryptography — PKC 2004. 2004. P. 55—68.
4. Oyono R. Arithmetik nichthyperelliptischer Kurven des Geschlechts 3 und ihre Anwendung in der Kryptographie : PhD Diss. Univ. DuisburgEssen, 2005....

Konigsberg Cyrillic editions of the calendars of the 1720s in the collection of the Russian State Library
... the field of calendarchronological of his time that performed practical and educational functions. The calendar for 1727 included the original author's text of the "Home Healer", and the calendar for 1730 included the first chapter of the arithmetic textbook. Three copies of calendars from the collection of the RSL contain readers’ comments on the margins, their ex libris, which is a certain sign of the cultural value.
1. Бондар Н. Рідкісні календарні видання ...

How to extract formulas from Pascal's triangle to find all primes
In the presented arithmetic study, the existence of an infinite set of numerical properties of a rightangled Pascal triangle is confirmed and the main results of finding its numerical discriminant are given. Exactly, the numerical properties of the truncated Pascal ...

About one algorithm of calculation of inverses in finite fields
... Panario. CRC Press, Taylor & Francis Group, 2013.
3. Itoh T., Tsujii S. A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases, Inform. and Comput. 1988. Vol. 78. P. 171—177.
4. Jungnickel D. Finite fields: Structure and Arithmetics. Mannheim ; Leipzig ; Wien ; Zürich, 1993.
5. Lidl R., Niederreiter H. Finite fields (Second edition). Cambridge University Press, 1997.
Aleshnikov S., Aleshnikova M., Gorbachev A.
finite field, multiplication, inversion, normal basis,...

Efficient algorithms for computing superelliptic curves
Represents basics algorithms of arithmetics superelliptic curves and optimal parameters superelliptic curve suitable for cryptography.
1.Koblitz N. Elliptic curve cryptosystems // Mathematics of Computation. 1987. № 48 (177). P. 203–209.
2. ANSI X9.63 Public Key Cryptography for ...

An analysis of the resistance of McEliece CS based on an AGcode to quantum Fourier sampling attack
... (дата обращения: 12.02.2015).
4. Stichtenoth H. On automorphisms of geometric Goppa codes // Journal of Algebra. 1990. № 130(1). P. 113—121.
5. Stichtenoth H. Algebraic function fields and codes. Springer, 2008.
6. Silverman J. Arithmetic of elliptic curves. Springer, 2009.
Ilyashenko I.
quantum algorithm, postquantum cryptography, elliptic curves, AGcodes.
120124

Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field
... curves // Cryptology ePrint Archive. 2008.
6.
Ravnshoj C. R.
Noncyclic subgroups of Jacobians of genus two curves // Ibid.
7.
Ravnshoj C. R.
Noncyclic subgroups of Jacobians of genus two curves with complex multiplication // Ibid.
8.
Dechene I.
Arithmetic of generalized Jacobians // Ibid. 2006.
9.
Dechene I.
On the security of generalized Jacobian cryptosystems // Ibid.
10.
Galbraith S. D., Smith B. A.
Discrete logarithms in generalized Jacobians // Ibid.
11.
Nagao K.
Improvement of th
...

On digitalization of the Kaliningrad region as an economic security element
... conditions for digital transformation. In this regard, the purpose of this study is to assess some quantitative indicators reflecting the readiness of the region's economy for digitalization. For this purpose, the integral index is calculated as the arithmetic mean of 8 subindices characterizing the technological provision of enterprises in the region and the affordability of information and communication technologies for them, human resources of the digital economy, the presence of a digital ...

Formal Languages and Automata V: Conway SemiringSemimodule Pairs and Finite Automata
... these linear systems with the behavior of nite automata over quemirings.
5. Bloom St. L., Esik Z. Iteration theories. EATCS Monographs on Theoretical Computer Science. Springer, 1993.
6. Buechi J. R. On a decision method in restricted second order arithmetic //Proc. Int. Congr. Logic, Methodology and Philosophy of Science. 1962. P. 111.
7. Conway J. H. Regular algebra and nite machines. Chapman & Hall, 1971.
8. Elgot C. Matricial theories // J. Algebra. 1976. N 42. P. 391422.
9. Esik Z., Kuich ...

Acceleration of Computations in Jacobian Hyperelliptic Curve
... Proceedings of the 2000 Symposium on Cryptography and Information Security. 2000. Р. 26—28.
2. Joux A. A OneRound Protocol for Tripartite DiffeHellman // Algorithmic Number Theory Symposium. SpringerVerlag, 2000. Р. 385—394.
3. Lange T. Formulae for Arithmetic on Genus 2 Hyperelliptic Curves // Applicable Algebra in Engineering, Communication and Computing. 2005. Vol. 15, iss. 5. P. 295—328.
4. Choie Y., Lee E. Implementation of Tate Pairing on Hyperelliptic Curve of Genus 2 // Information ...

Formal Languages and Automata VI:algebraic systems and transducers
... power series.
6. Berstel J. Transductions and ContextFree Languages.
7. Bloom St. L., Esik Z. Iteration Theories. EATCS Monographs on Theoretical Computer Science. Springer, 1993.
8. Bychi J. R. On a decision method in restricted second order arithmetic // Proc. Int. Congr. Logic, Methodology and Philosophy of Science, 1960. Stanford University Press, 1962. P. 111.
9. Cohen R. S., Gold A. Y. Theory of !languages I: Characterizations of !contextfree languages // JCSS. 15(1977). P. 169184....

Why is the space around us three dimensional
... attempts to find an answer to this question, by remaining only within the mathematics, are bound to fail. On the contrary, it is in the present math study that it is shown that why space is threedimensional can only be explained only by means of higher arithmetic. This is followed by an answer to the following important question. Where and how the loss and subsequent recovery of symmetry in spatial numerical figures occurs. Why is there a loss of stable numerical symmetry? The present arithmetic ...

A transcendental analysis of mathematics: The constructive nature of mathematics
... Aristotle, 2011, in: Shiffman, M. De Anima: On the Soul, (Newburyport, MA: Focus Publishing.
2. Frege, G. 1884, Die Grundlagen der Arithmetik: eine logischmathematische Untersuchung über den Begriff der Zahl. Breslau. (English: The Foundations of Arithmetic: the logicalmathematical Investigation of the Concept of Number).
3. Galileiy, G, 1964,Izbrannye trudy v 2 t. M.: Nauka, 1964. v.1.
4. Galileiy, G., 1987, Probirnyh del master. M. Nauka.
5. Gil'bert. D., 1998, Aksiomaticheskoe myshlenie //Ego ...

A transcendental analysis of mathematics: The abstract nature of mathematical knowledge
... http://iph.ras.ru/elib/0019.html22. Plato. 1993, Republic [Republic]. In: Sobranie sochineniy v 4 t., Moscow. T. 3, s. 79—420.23. Frege, G. 2000, Osnovopoloj`enija arifmetiki (logikomatematicheskoe issledovanie ponjatija chisla) [The Foundations of Arithmetic]. Tomsk.24. Hintikka, J. A. 1980, Poverhnostnaja informacija i glubinnaja informacija [Surface Information and Depth Information]. In: Logikoepistemologicheskie issledovanij’ [LogicoEpistemologic Research]. Moscow, s. 182—228.25. Hume,...