Results 71 to 80 of about 20,685 (194)
On the Diophantine equation x2+p2k+1=4yn
International Journal of Mathematics and Mathematical Sciences, 2002 It has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x ...
S. Akhtar Arif, Amal S. Al-Ali
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Journal of Geophysical Research: Space Physics, Volume 131, Issue 3, March 2026.Abstract The wave telescope is an analysis technique for multi‐point spacecraft data that estimates power spectra in reciprocal position space (k $k$‐space). It has been used to reveal the spatial properties of waves and fluctuations in space plasmas. Originally designed as an analysis tool for 4 spacecraft constellations, new multi‐scale missions such
L. Schulz +7 more
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On the Diophantine equation Ax2+22m=yn
International Journal of Mathematics and Mathematical Sciences, 2001 Let h denote the class number of the quadratic field ℚ(−A) for a square free odd integer A>1, and suppose that n>2 is an odd integer with (n,h)=1 and m>1.
Fadwa S. Abu Muriefah
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Linear Diophantine equations and conjugator length in 2‐step nilpotent groups
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract We establish upper bounds on the lengths of minimal conjugators in 2‐step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp.
M. R. Bridson, T. R. Riley
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Diophantine Equation 4k2−1nx+4kny=4k2+1nz
Journal of MathematicsLet a,b,c be a primitive Pythagorean triple such that a2+b2=c2 with 2b. In 1956, L. Jesmanowicz conjectured that, for any positive integer n, the equation anx+bny=cnz has only the positive solution x,y,z=2,2,2. In 1959, Lu Wenduan claimed that if n=1 and
Nai-juan Deng, Ridi Huang
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The diophantine equation ni+1=k(dn−1)
International Journal of Mathematics and Mathematical Sciences, 1989 The Diophantine equation of the title is solved for i=3,4 and an infinite family of solutions were found for i≥5.
Steve Ligh, Keith Bourque
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Arithmetic progressions at the Journal of the LMS
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the papers P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. (1) 11 (1936), 261–264 and K. F. Roth, On certain sets of integers, J. London Math. Soc. (1) 28 (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.
Ben Green
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Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
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On the Diophantine equation x2+2k=yn
International Journal of Mathematics and Mathematical Sciences, 1997 By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved.
S. Akhtar Arif, Fadwa S. Abu Muriefah
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Optimising Wave Energy Plant Location Through Neutrosophic Multi‐Criteria Group Decision‐Making
CAAI Transactions on Intelligence Technology, Volume 11, Issue 1, Page 167-189, February 2026.ABSTRACT The global shift towards sustainable energy has intensified research into renewable sources, particularly wave energy. Pakistan, with its long coastline, holds significant potential for wave energy development. However, identifying optimal locations for wave energy plants involves evaluating complex, multi‐faceted criteria.
Hafiz Muhammad Athar Farid +4 more
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