Results 1 to 10 of about 9,936 (110)
Quantitative results on Diophantine equations in many variables [PDF]
Acta Arithmetica, 2020 We consider a system of integer polynomials of the same degree with non-singular local zeros and in many variables. Generalising the work of Birch (1962) we find quantitative asymptotics (in terms of the maximum of the absolute value of the coefficients of these polynomials) for the number of integer zeros of this system within a growing box.
van Ittersum, Jan-Willem M.
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Optimization of the multivariate polynomial public key for quantum safe digital signature [PDF]
Scientific Reports, 2023 Kuang, Perepechaenko, and Barbeau recently proposed a novel quantum-safe digital signature algorithm called Multivariate Polynomial Public Key or MPPK/DS.
Randy Kuang, Maria Perepechaenko
doaj +2 more sources
Diophantine triples in linear recurrences of Pisot type. [PDF]
Res Number Theory, 2018 The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence or finiteness
Fuchs C, Hutle C, Luca F.
europepmc +5 more sources
Counting monochromatic solutions to diagonal Diophantine equations
Discrete Analysis, 2021 Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis 2021:14, 47 pp. An important subfield of Ramsey theory concerns questions of the following type: for which systems of equations $E_1,\dots,E_k$ in variables $x_1,\dots,
Sean Prendiville
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On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory [PDF]
Journal of Fuzzy Extension and ApplicationsIntegers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia.
Mohammad Abobala +2 more
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Diophantine equations in moderately many variables [PDF]
Michigan Mathematical Journal, 2016 We give upper bounds for the number of integral solutions of bounded height to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where the $f_i$ are polynomials with integer coefficients. The estimates are obtained by generalising an approach due to Heath-Brown, using a certain $q$-analogue of van der Corput's method, to the case of ...
openaire +4 more sources
Hilbert's 10th Problem for solutions in a subring of Q [PDF]
, 2019 Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many ...
Peszek, Agnieszka, Tyszka, Apoloniusz
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Combinatorial Diophantine equations and a refinement of a theorem on separated variables equations [PDF]
, 2013 We look at Diophantine equations arising from equating classical counting functions such as perfect powers, binomial coefficients and Stirling numbers of the first and second kind.
Bilu, Yuri F. +3 more
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Diophantine equations in semiprimes
Discrete Analysis, 2019 Diophantine equations in semiprimes, Discrete Analysis 2019:17, 21 pp. This paper considers the problem of finding integer solutions to integral polynomial equations of the form $$f(x_1,\dots,x_n)=0\qquad\qquad (*)$$ with the condition that each ...
Shuntaro Yamagishi
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Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0 [PDF]
, 2009 Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$, not equal to $K$. We prove the following undecidability results for $R$: If $K$ is recursive, then Hilbert's Tenth Problem is ...
Moret-Bailly, Laurent +1 more
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