Results 11 to 20 of about 93 (91)
Simultaneous diophantine approximation [PDF]
Bulletin of the Australian Mathematical Society, 1972 AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
openaire +3 more sources
New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method
Cryptography, 2018 This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = p q in polynomial time. The paper has two parts.
Muhammad Rezal Kamel Ariffin +3 more
doaj +1 more source
Simultaneous inhomogeneous diophantine approximation on manifolds [PDF]
Journal of Mathematical Sciences, 2012 Dedicated to A.O.
Beresnevich, V. V., Velani, S. L.
openaire +3 more sources
On simultaneous inhomogeneous Diophantine approximation [PDF]
Acta Arithmetica, 2006 In this paper, the authors study inhomogeneous problems in metrical Diophantine approximation. For a tuple \(\underline{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb R}^k\) and real numbers \(v,w>0\), let \({\mathcal V}_v(\underline{\alpha})\) denote the set of \(\xi \in {\mathbb R}\) for which there is a \(c > 0\) such that the inequality ...
Bugeaud, Yann, Chevallier, Nicolas
openaire +3 more sources
Simultaneous diophantine approximation with square-free numbers [PDF]
Acta Arithmetica, 1993 A set \(\alpha_ 1,\dots,\alpha_ s\) of real numbers is said to be weakly compatible if \(\sum_{j=1}^ s \ell_ j \alpha_ j=u/v\) with \((u,v)=1\) implies that \(v\) is square-free. This condition is necessary and sufficient for \[ \liminf_{\mu^ 2(n)=1} \max_ j\|\alpha_ j n\|=0, \] where \(\|\cdot\|\) denotes the fractional part, as usual.
Baker, Roger C. +2 more
openaire +3 more sources
Successful cryptanalysis on RSA type modulus N=p2q
e-Prime: Advances in Electrical Engineering, Electronics and EnergyAs internet technology advances and our interactions increasingly take place online, cryptography emerges as a valuable tool to address security concerns. Cryptography serves as a means to guarantee the protection of privacy and confidential information,
Normahirah Nek Abd Rahman
doaj +1 more source
Successive Minima and Best Simultaneous Diophantine Approximations [PDF]
Monatshefte für Mathematik, 2005 8 ...
Aliev, Iskander, Henk, Martin
openaire +2 more sources
Simultaneous diophantine approximation of rational numbers [PDF]
Acta Arithmetica, 1972 For any real number \(x\), let \(\Vert x\Vert\) denote the distance from \(x\) to the nearest integer. Let \(n\) be any positive integer and let \(\sigma = (s_1, \ldots, s_n)\) denote an arbitrary point in the set \(S^n\) of \(n\)-dimensional points all of whose coordinates are rational noninteger numbers.
openaire +2 more sources
Liminf Sets in Simultaneous Diophantine Approximation [PDF]
Journal de théorie des nombres de Bordeaux, 2017 Let 𝒬 be an infinite set of positive integers. Denote by W τ,n * (𝒬) the set of n–tuples of real numbers simultaneously τ–well approximable by infinitely many rationals with denominators in 𝒬 but by only finitely many rationals with denominators in the complement of 𝒬.
openaire +6 more sources
Simultaneous Diophantine approximation and VIP systems [PDF]
Acta Arithmetica, 2005 Summary: A subset \(E\) of \(\mathbb Z\) is said to be \(\text{IP}^*\) if for any sequence \((x_n)\) in~\(\mathbb Z\) one has ...
Bergelson, Vitaly +2 more
openaire +2 more sources