Results 11 to 20 of about 12,497 (156)
Open Computer Science, 2017 Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
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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.
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On two Diophantine inequalities over primes [PDF]
Indagationes Mathematicae, 2018 21 ...
Zhang, Min, Li, Jinjiang
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Cubic Diophantine inequalities [PDF]
Mathematika, 1982 \textit{H. Davenport} and \textit{K. F. Roth} [Mathematika, 2, 81--96 (1955; Zbl 0066.29301)] showed that for \(s \geq 8\) the values of the real additive form \(\lambda_1 x^3_1 + \ldots + \lambda_s x^3_s\) on \(\mathbb{Z}^s\) are dense on the real line, provided that \(\lambda_1/ \lambda_2\) is irrational.
Baker, R. C. +2 more
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On a Diophantine Inequality with s Primes
Journal of Mathematics, 2021 Let ...
Xiaofei Yan, Lu Zhang
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Mathematics, 2021 Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all ...
S. Subburam +6 more
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On the Multiplicity of a Proportionally Modular Numerical Semigroup
Discrete Dynamics in Nature and Society, 2021 A proportionally modular numerical semigroup is the set Sa,b,c of nonnegative integer solutions to a Diophantine inequality of the form ax mod b≤cx, where a,b, and c are positive integers.
Ze Gu
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DIOPHANTINE INEQUALITIES OF FRACTIONAL DEGREE [PDF]
Mathematika, 2021 Accepted for publication in ...
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One Diophantine inequality with unlike powers of prime variables
Journal of Inequalities and Applications, 2016 In this paper, we show that if λ 1 $\lambda_{1}$ , λ 2 $\lambda_{2}$ , λ 3 $\lambda_{3}$ , λ 4 $\lambda _{4}$ , λ 5 $\lambda_{5}$ are nonzero real numbers not all of the same sign, η is real, 0 < σ < 1 720 ...
Wenxu Ge, Weiping Li
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On the existence of $S$-Diophantine quadruples [PDF]
, 2018 Let $S$ be a set of primes. We call an $m$-tuple $(a_1,\ldots,a_m)$ of distinct, positive integers $S$-Diophantine, if for all $i\neq j$ the integers $s_{i,j}:=a_ia_j+1$ have only prime divisors coming from the set $S$, i.e.
Ziegler, Volker
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