Results 91 to 100 of about 33,591 (180)
On the Relationship Between Matiyasevich's and Smorynski's Theorems
Scientific Annals of Computer Science, 2019 Let R be a non-zero subring of Q with or without 1. We assume that for every positive integer n there exists a computable surjection from N onto Rn. Every R \in {Z,Q} satisfi es these conditions.
Agnieszka Peszek, Apoloniusz Tyszka
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Iitaka fibrations and integral points: A family of arbitrarily polarized spherical threefolds
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analog of Iitaka fibrations, which have not yet been adequately
Ulrich Derenthal, Florian Wilsch
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Journal of Computer Assisted Learning, Volume 41, Issue 5, October 2025.ABSTRACT Background Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming‐based mathematical problem‐solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes.
Huiyan Ye, Biyao Liang, Oi‐Lam Ng
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Symmetric Diophantine systems [PDF]
Acta Arithmetica, 1991 By an ingenious, elementary method the author solves completely systems of diophantine equations like \[ x_ 1+x_ 2+x_ 3=y_ 1+y_ 2+y_ 3,\qquad x_ 1x_ 2x_ 3=y_ 1y_ 2y_ 3 \] or \[ x_ 1^ 3+x_ 2^ 3+x_ 3^ 3=y_ 1^ 3+y_ 2^ 3+y_ 3^ 3,\qquad x_ 1^ 2+x_ 2^ 2+x_ 3^ 2=y_ 1^ 2+y_ 2^ 2+y_ 3^ 2. \] His only predecessors seem to be \textit{A.
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Restricted diophantine approximation [PDF]
Journal of the Australian Mathematical Society, 1977 AbstractThe problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.
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From Diophantine approximations to Diophantine equations
Keldysh Institute Preprints, 2016 Summary: Let in the real \(n\)-dimensional space \(\mathbb{R}^n=\{X\}\) be given \(m\) real homogeneous forms \(f_i(X), i=1,\dotsc,m, 2\leqslant m\leqslant n\). The convex hull of the set of points \(G(X)=(|f_1(X)|,\dotsc,|f_m(X)|)\) for integer \(X\in\mathbb Z^n\) in many cases is a convex polyhedral set. Its boundary for \(||X||
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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.
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International Journal of Mathematics and Mathematical Sciences, 1986 It is shown how to find all integers a, b such that a + b, a2 + b2 and a3 + b3 are simultaneously perfect squares.
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A note on the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 [PDF]
Notes on Number Theory and Discrete MathematicsWe prove that, for k≥10, the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 in positive integers x, y, z, k with z>1, has no solutions satisfying ...
Yangcheng Li
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Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
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