Results 11 to 20 of about 81,722 (194)
On a Fermat-Type Diophantine Equation
Journal of Number Theory, 2000 Let p>3 be an odd prime and ζ a pth root of unity. Let c be an integer divisible only by primes of the form kp−1, (k, p)=1. Let C(i)p be the eigenspace of the ideal class group of Q(ζ) corresponding to ωi, ω being the Teichmuller character.
Sitaraman, Sankar
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On Meromorphic Solutions of Functional Equations of Fermat Type [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2018 15pages ...
Hu, Pei-Chu, Wang, Qiong
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An application of the symplectic argument to some Fermat-type equations
Comptes Rendus. Mathématique, 2016 Let p be a prime number. In the early 2000s, it was proved that the Fermat equations with coefficients 3 x
Freitas, Nuno, Kraus, Alain
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The fermat equation over quadratic fields
, 1984 Kummer's method of proof is applied to the Fermat equation over quadratic fields. The concept of an m-regular prime, p, is introduced and it is shown that for certain values of m, the Fermat equation with exponent p has no nontrivial solutions over the ...
Parry, Charles J., Hao, Fred H.
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Data supporting Extended Fermat Equation
, 2018 <p>Data supporting draft paper "Prabhakar, Giri. (2018, June 20). On Triangles as Real Analytic Varieties of an Extended Fermat Equation (Version Draft). Zenodo.
Prabhakar, Giri (5455286) +1 more
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, 2004 We study solutions of the Fermat equation defined over Q(2), and prove a version of `Fermat's Last Theorem' over Q(2), assuming an unpublished result of ...
Meekin, Paul, Jarvis, Frazer
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The generalized fermat equation in function fields
, 1991 We show that if r > n!(n! − 2) the set of solutions xj ∈ C(t) of a Fermat equation Σ1najxjr = 0, aj ∈ C(t), is the union of at most n!n! families with an explicitly given simple structure.
Bombieri, E., Mueller, J.
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Note on a Fermat-type diophantine equation
Journal of Number Theory, 2003 The author extends his previous results [J.\ Number Theory 80, 174-186 (2000; Zbl 0972.11015)] concerning the Diophantine equation \(x^p+y^p=cpz^p\), where \(p\) is an odd prime and the prime factors of \(c\) are of the form \(kp-1\) with \((k,p)=1\). Let \(x,y,z\) be a solution. Then, as shown by the author [op. cit.], \(p\) is irregular.
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Guiding and Manipulating Light Fields in Microstructured Liquid Crystals
Advanced Physics Research, EarlyView.This review summarizes recent advances in guided‐wave optics enabled by microstructured liquid crystal (LC) devices, covering their fundamental material properties, key degree of freedom for dynamic light field manipulations. The advances of linear guided‐wave optics, nonlinear‐optics with spatial optical solitons, and microlasers in LC‐based devices ...
Shan‐shan Chang +2 more
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On the existence of solutions of a Fermat-type difference equation
Annales Academiae Scientiarum Fennicae Mathematica, 2015 Let \(F_C(n)\) be the smallest positive integer \(k\) such that \[ f_1^n+f_2^n+\cdots+f_k^n=1 \] has a solution consisting of \(k\) non-constant functions \(f_1,f_2,\dots,f_k\) in the field (or ring) \(C\). In their comprehensive review article, \textit{G. G. Gundersen} and \textit{W. K. Hayman} [Bull. Lond. Math. Soc.
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