On the Relationship Between Matiyasevich's and Smorynski's Theorems [PDF]
Scientific Annals of Computer Science, 2019 Let R be a non-zero subring of Q with or without 1. We assume that for every positive integer n there exists a computable surjection from N onto Rn. Every R \in {Z,Q} satisfi es these conditions.
Agnieszka Peszek, Apoloniusz Tyszka
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Diophantine equations in two variables [PDF]
, 2002 This is an expository lecture on the subject of the title delivered at the Park-IAS mathematical institute in Princeton (July, 2000).Comment: Not for separate ...
Kim, Minhyong
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On the System of Diophantine Equations x2-6y2=-5 and x=az2-b [PDF]
The Scientific World Journal, 2014 Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x,y,z) of the system of Diophantine equations x2-6y2=-5 and x=2z2-1. In this paper, we extend this result and put forward a generalized method which can completely solve ...
Silan Zhang, Jianhua Chen, Hao Hu
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S-Restricted Compositions Revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years.
Behrouz Zolfaghari +2 more
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Diophantine imaging reveals the broken symmetry of sums of integer cubes [PDF]
Scientific ReportsWe introduced a novel method for visualizing large diophantine datasets and in particular found that mapping the known integer triplets $$\{a,b,c\}$$ { a , b , c } solving either equations of the type $$a^3+b^3+c^3=d$$ a 3 + b 3 + c 3 = d or $$a^3+b^3+c ...
Eldar Sultanow +2 more
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Research and development of the mathematic models of cryptosystems based on the universal Diophantine language [PDF]
SHS Web of Conferences, 2022 This paper shows the objective necessity of improving the information security systems under the development of information and telecommunication technologies.
Osipyan V.O., Litvinov K.I., Zhuck A.S.
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From Diophantian Equations to Matrix Equations (III) - Other Diophantian Quadratic Equations and Diophantian Equations of Higher Degree [PDF]
Educaţia 21, 2023 In this paper, we propose to continue the steps started in the first two papers with the same generic title and symbolically denoted by (I) and (II), namely, the presentation of ways of achieving a systemic vision on a certain mathematical notional ...
Teodor Dumitru Vălcan
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Hilbert's Tenth Problem in Coq (Extended Version) [PDF]
Logical Methods in Computer Science, 2022 We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory.
Dominique Larchey-Wendling +1 more
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Solution to a pair of linear, two-variable, Diophantine equations with coprime coefficients from balancing and Lucas-balancing numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let Bₙ and Cₙ be the n-th balancing and Lucas-balancing numbers, respectively. We consider the Diophantine equations ax + by = (1/2)(a - 1)(b - 1) and 1 + ax + by = (1/2)(a - 1)(b - 1) for (a,b) ∈ {(Bₙ,Bₙ₊₁), (B₂ₙ₋₁,B₂ₙ₊₁), (Bₙ,Cₙ), (Cₙ,Cₙ₊₁)} and ...
R. K. Davala
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Diophantine problems in solvable groups [PDF]
Bulletin of Mathematical Sciences, 2020 We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions.
Albert Garreta +2 more
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