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On a Diophantine Inequality with s Primes

Journal of Mathematics, 2021
Let ...
Xiaofei Yan, Lu Zhang
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On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

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, Lewis Nkenyereye, N. Anbazhagan, S. Amutha, M. Kameswari, Woong Cho, Gyanendra Prasad Joshi   +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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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 some diophantine equations involving factorials [PDF]

Mathematica Bohemica
We study the Diophantine equations $(n!)^k - n^k = (k!)^n - k^n$ and $(n!)^k + n^k = (k!)^n + k^n$, where $k$ and $n$ are positive integers. According to H. Arzel, F. Luca (2017), only the first equation has nontrivial solutions. It is proved also that ${
Maciej Gnatowski
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Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

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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Observation of vibrating systems at different time instants

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of A. Szijártó and J.
Ambroise Vest
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From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges

Discrete Analysis, 2017
From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges, Discrete Analysis 2017:10, 25 pp. A basic fact in the theory of Diophantine approximation is Dirichlet's theorem that for every real number ...
Michael Boshernitzan, Vincent Delecroix
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A Diophantine Inequality Involving Mixed Powers of Primes with a Specific Type

Mathematics
Let λ1,λ2,λ3 be nonzero real numbers, not all of the same sign; let λ1/λ2 be irrational; and let η be any real number. We investigate the solvability of the inequality |λ1p1+λ2p2+λ3p32+η|0 in the prime variables p1, p2, and p3.
Tatiana L. Todorova, Atanaska Georgieva
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A ternary Diophantine inequality with prime numbers of a special form

Periodica Mathematica Hungarica, 2021
Min Zhang, Jinjiang Li
exaly