Results 71 to 80 of about 92,931 (194)
Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
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The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
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SOLUTION OF THE EXPONENTIAL DIOPHANTINE EQUATION 10^X + 400^Y=Z^2
International Journal of Latest Technology in Engineering, Management & Applied ScienceDiophantine equations are so important in solving important real-world problems like network flow problems, pole placement problems, business investment problems, and data privacy problems that researchers are becoming more interested in developing new ...
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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A note on the exponential Diophantine equation (aˣ - 1) (bʸ - 1) = az²
Annales Mathematicae et Informaticae. Let a, b be fixed positive integers such that ( a mod 8 , b mod 8) ∈ { (0 , 3) , (0 , 5) , (2 , 3) , (2 , 5) , (4 , 3) , (6 , 5) } . In this paper, using elementary meth-ods with some classical results for Diophantine equations, we prove the following ...
Y. Fujita, Maohua Le
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Diophantine Equation 41k2−nx+4kny=41k2+nz
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let (a, b, c) be a primitive Pythagorean triple such that a2 + b2 = c2 with 2|b. In 1956, L. Jesmanowicz conjectured that, for any positive integer n, the equation (an)x + (bn)y = (cn)z has only the positive solution (x, y, z) = (2, 2, 2). In 1959, Lu Wenduan claimed that if n = 1 and (a, b, c) = (4k2 − 1, 4k, 4k2 + 1), then the conjecture is true ...
Nai-juan Deng +2 more
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Euclidean algorithms are Gaussian over imaginary quadratic fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We prove that the distribution of the number of steps of the Euclidean algorithm of rationals in imaginary quadratic fields with denominators bounded by N$N$ is asymptotically Gaussian as N$N$ goes to infinity, extending a result by Baladi and Vallée for the real case.
Dohyeong Kim, Jungwon Lee, Seonhee Lim
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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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A circle method approach to K‐multimagic squares
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract In this paper, we investigate K$K$‐multimagic squares of order N$N$. These are N×N$N \times N$ magic squares that remain magic after raising each element to the k$k$th power for all 2⩽k⩽K$2 \leqslant k \leqslant K$. Given K⩾2$K \geqslant 2$, we consider the problem of establishing the smallest integer N2(K)$N_2(K)$ for which there exist ...
Daniel Flores
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On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]
Ramanujan J, 2021 Ddamulira M, Luca F.
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