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The integer part of nonlinear forms with prime variables
AIMS Mathematics, 2022 In this paper, we discuss problems that integer part of nonlinear forms with prime variables represent primes infinitely. We prove that under suitable conditions there exist infinitely many primes $ p_j, p $ such that $ [\lambda_1p_1^2+\lambda_2p_2^2 ...
Weiping Li, Guohua Chen
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A Diophantine Problem with Unlike Powers of Primes
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 Let k be an integer with 4 ≤ k ≤ 6 and η be any real number. Suppose that λ1, λ2, …, λ5 are nonzero real numbers, not all of them have the same sign, and λ1/λ2 is irrational. It is proved that the inequality λ1p1+λ2p22+λ3p33+λ4p44+λ5p5k+η
Quanwu Mu, Liyan Xi, Tingting Wang
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Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
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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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The integral part of a nonlinear form with a square, a cube and a biquadrate
Open Mathematics, 2020 In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
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A note on Diophantine inequalities in function fields [PDF]
Notes on Number Theory and Discrete MathematicsWe will discuss how the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn circle method can be used to study 𝔽_q[t] solutions to inequalities of the form ord(λ₁p₁ᵏ+...+λₛpₛᵏ-γ)
Kathryn Wilson
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On the Olson and the Strong Davenport constants [PDF]
, 2010 A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant.
Ordaz, Oscar +3 more
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A Diophantine approximation problem with two primes and one k-power of a prime [PDF]
, 2018 We refine a result of the last two Authors on a Diophantine approximation problem with two primes and a k-th power of a prime which was only proved to hold for ...
Alessandro, Gambini +2 more
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On Diophantine approximation by unlike powers of primes
Open Mathematics, 2019 Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0.
Ge Wenxu, Li Weiping, Wang Tianze
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