Results for 'primes of the form n^2+1'

13 found
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  1.  10
    Historical and Foundational Details on the Method of Infinite Descent: Every Prime Number of the Form 4 N + 1 is the Sum of Two Squares.Paolo Bussotti & Raffaele Pisano - 2020 - Foundations of Science 25 (3):671-702.
    Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the (...)
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  2.  60
    Rock ‘N’ Labels: Tracking the Australian Recording Industry in ‘The Vinyl Age’: Part Two: 1970–1995, and After.Clinton J. Walker, Trevor Hogan & Peter Beilharz - 2012 - Thesis Eleven 110 (1):112-131.
    Over the past 50 years, rock music has been the prime mover of an emergent national recording industry in Australia. This is a story in turn of increasing size, complexity, diversity, and sophistication, before its ultimate decline into the 21st century. This story has not been told in full previously and this article is a first step to make good this gap in the historical and cultural sociology of popular music. In this study, which has two parts, we survey record (...)
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  3.  47
    Characterization of Prime Numbers in Łukasiewicz's Logical Matrix.Alexander S. Karpenko - 1989 - Studia Logica 48 (4):465 - 478.
    In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the natural series. Further, we introduce (...)
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  4.  17
    Being and Creation in the Theology of John Scottus Eriugena: An Approach to a New Way of Thinking.Sergei N. Sushkov - unknown
    The work aims to demonstrate that at the heart of Eriugena’s approach to Christian theology there lies a profoundly philosophical interest in the necessity of a cardinal shift in the paradigms of thinking – namely, that from the metaphysical to the dialectical one, which wins him a reputation of the ‘Hegel of the ninth century,’ as scholars in Post-Hegelian Germany called him. The prime concern of Eriugena’s discourse is to prove that the actual adoption of the salvific truth of Christ’s (...)
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  5. The Pursuit of the Riemann Hypothesis.Mark Colyvan - unknown
    With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address (...)
     
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  6.  15
    The Theory of Liouville Functions.Pascal Koiran - 2003 - Journal of Symbolic Logic 68 (2):353-365.
    A Liouville function is an analytic function $H : C \rightarrow C$ with a Taylor series $\Sigma_{n=1}^\infty x^n/a_n$ such the $a_n\prime s$ form a "very fast growing" sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H.
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  7.  34
    Rings Which Admit Elimination of Quantifiers.Bruce I. Rose - 1978 - Journal of Symbolic Logic 43 (1):92-112.
    We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy ≠ 0). Theorem (...)
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  8.  1
    Cyclotomie et formes quadratiques dans l’œuvre arithmétique d’Augustin-Louis Cauchy.Jenny Boucard - 2013 - Archive for History of Exact Sciences 67 (4):349-414.
    Augustin-Louis Cauchy publie une majorité de ses recherches arithmétiques entre 1829 et 1840. Celles-ci ne sont pourtant qu’évoquées dans certaines histoires de la théorie des nombres centrées sur les lois de réciprocité ou sur la théorie des nombres algébriques. Elles y sont décrites comme contenant quelques résultats similaires à ceux de Gauss, Jacobi ou Dirichlet mais de manière incomplète et désordonnée. L’objectif de cet article est de présenter une analyse des textes arithmétiques de Cauchy publiés entre 1829 et 1840 pour (...)
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  9.  6
    A Companion to Heidegger’s Introduction to Metaphysics. [REVIEW]Miles Groth - 2002 - Review of Metaphysics 56 (2):452-454.
    The coterie of commentators represented in the present volume include some of the clearest voices for Heidegger’s way of thinking among the second and third generations of American Heidegger scholars. Two of the contributors, who are also the volume’s editors, have just published a new translation of Einführung in die Metaphysik, an event that would appear to be one of the reasons for the project published here. Its thirteen essays are organized under three headings: the question of being, Heidegger and (...)
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  10. Objects as Temporary Autonomous Zones.Tim Morton - 2011 - Continent 1 (3):149-155.
    continent. 1.3 (2011): 149-155. The world is teeming. Anything can happen. John Cage, “Silence” 1 Autonomy means that although something is part of something else, or related to it in some way, it has its own “law” or “tendency” (Greek, nomos ). In their book on life sciences, Medawar and Medawar state, “Organs and tissues…are composed of cells which…have a high measure of autonomy.”2 Autonomy also has ethical and political valences. De Grazia writes, “In Kant's enormously influential moral philosophy, autonomy (...)
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  11. Implicit Memory: History and Current Status.Daniel L. Schacter - 1987 - Journal of Experimental Psychology 13 (3):501-18.
    Je lui ai associÉ un court extrait d'une revue de questions portant sur le même thème. Implicit memory is revealed when previous experiences facilitate perf on a task that does not require conscious or intentional recollection of those expces. Explicit memory is revealed when perf on a task requires conscious recolelction of previous expces. Il s'agit de defs descriptives qui n'impliquent pas l'existence de deux systs de mÉmo sÉparÉs. Historiquement Descartes est le premier ˆ faire mention de phÉnomènes de mÉmo (...)
     
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  12.  5
    Effective Inseparability, Lattices, and Preordering Relations.Uri Andrews & Andrea Sorbi - forthcoming - Review of Symbolic Logic:1-28.
    We study effectively inseparable prelattices $\wedge, \vee$ are binary computable operations; ${ \le _L}$ is a computably enumerable preordering relation, with $0{ \le _L}x{ \le _L}1$ for every x; the equivalence relation ${ \equiv _L}$ originated by ${ \le _L}$ is a congruence on L such that the corresponding quotient structure is a nontrivial bounded lattice; the ${ \equiv _L}$ -equivalence classes of 0 and 1 form an effectively inseparable pair of sets). Solving a problem in we show, that (...)
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  13.  31
    Logical Consecutions in Discrete Linear Temporal Logic.V. V. Rybakov - 2005 - Journal of Symbolic Logic 70 (4):1137 - 1149.
    We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...)
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