Diophantine Equations
Multi-rate Ripple-Free Deadbeat Control for Nonlinear Systems Using Diophantine Equations
... apply Diophantine equations for well known transfer function and to decrease the length of the three polynomials that obtained from minimum order solution of Diophantine ...
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Cryptanalysis of a public key cryptosystem based on Diophantine equations via weighted LLL reduction
... security. Diophantine equations of degree increasing type is proved to be unsolvable in ...such Diophantine equations is expected to be the most difficult problem among the other problems which ...
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Three special systems of double diophantine equations
... solutions. In this context, one may refer (Gopalan et al, 2014; Gopalan et al, 2016; Gopalan et al, 2016; Gopalan et al, 2016; Meena et al, 2016; Gopalan et al, 2016; Devibala et al, 2017). The above results motivated us ...
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Modular and reciprocity approaches to a family of diophantine equations
... upon the theory of the modular approach to Diophantine equations. The ba- sic technique was previously developed by mathematicians like Hellegouarch [28], Frey [22], Mazur, Serre [36], and Ribet in the ...
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Methods of Solving Diophantine Equations in Secondary Education in Romania
... of Diophantine equations, presentation of first-degree Diophantine equations, Pythagorean triples and higher - Diophantine equations, methods for solving Diophantine ...
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On a few Diophantine equations, in particular, Fermat's last theorem
... some equations which have no solution at all, and you will come across some equations about which the only thing we know is that we know nothing about ...other Diophantine equations which were ...
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Characterizations for solutions of certain classes of Non-linear Diophantine equations
... ABSTRACT: The main aim of this paper is to introduce a method, to solve certain class of non-homogenous non- Linear Diophantine equations and investigate various properties using[r] ...
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Superconformal Block Quivers, Duality Trees and Diophantine Equations
... the Diophantine equation as the Tits form of the quiver, Seiberg duality is seen as affine Weyl reflections in the space of roots, provides a representation- theoretic approach - complementing the usual geometric ...
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Applications of Continued Fractions in Cryptography and Diophantine Equations
... The theory of continued fractions has applications in cryptographic problems and in so- lution methods for Diophantine equations. We will first examine the basic properties of continued fractions such as ...
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Diophantine equations with a finite number of solutions: Craig Smory´nski’s theorem, Harvey Friedman’s conjecture, and relative recursive enumerability
... which have at most k variables, where k > 9, see [7]. In section 3, we show that Smory´nski’s theorem easily follows from Matiyasevich’s theorem. In section 4, we show that Hilbert’s Tenth Problem for Q has a negative ...
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On some Diophantine equations
... Now, let us examine all solutions of the following equations by using Diophantine equations given in Theorem , Theorem , Theorem and the divisibility rules of the sequences un an[r] ...
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Contents. 6 Continued Fractions and Diophantine Equations. 6.1 Linear Diophantine Equations
... given Diophantine equation possesses any solutions, or (even if existence is known) for nding them ...solving Diophantine equations are rather ad hoc, and so our goals in this chapter are primarily ...
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A repulsion motif in Diophantine equations
... these equations was made by Siegel, who proved that a nonsingular plane cubic equation has only finitely many integral ...simple equations can have inordinately large integral solutions in comparison to the ...
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Effective Methods for Diophantine Equations
... of Diophantine equations, see the papers by Bilu [15],[16], the survey by Gy˝ory [42] and the book by Smart [81] and the references given ...only Diophantine quadruple of the form { 1, 3, 8, x } is { ...
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On Polynomials Solutions of Quadratic Diophantine Equations
... A Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers ...only. Diophantine problems have fewer equations than un- known variables and involve finding ...
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On Infinite Number of Solutions for one type of Non Linear Diophantine Equations
... Then the inevitable Prime Number Theorem which beautifully models the statistical behavioral pattern of huge primes viz., chance for an arbitrarily picked 𝑛𝜖𝑁 to be a prime number is inv[r] ...
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On a class of diophantine equations
... The only remaining possibilities for more solutions are where X or Y ∈ {−4, −3, −2, −1, 0} where there are no nontrivial solutions and the proof is completed.. Finally note that 6 has 16[r] ...
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Diophantine equations and identities
... Some new third and fifth degree combinatorial identities are derived from units in algebraic number fields... KEY WORDS AND PHRASES..[r] ...
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Diophantine equations in positive characteristic
... from diophantine approximation. Most of the methods from diophantine approximation can not be transferred to positive characteristic, so that this is possible with the method of Beukers and Schlickewei is a ...
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Gauss' algorithm for the solution of quadratic diophantine equations
... The nunber of reduced forms in a period of rJuced forms of determinantperiod of the classical continued fractio^ ii lf,"-n.*U"r of terms in the expansion of an appropriate quadratic irra[r] ...
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