Results 61 to 70 of about 651 (161)
On The Number Of Solutions To The Generalized Fermat Equation
, 2007 . We discuss the maximum number of distinct non-trivial solutions that a generalized Fermat equation Ax n + By n = Cz n might possibly have. The abc- conjecture implies that it can never have more than two solutions once n ? n 0 (independent of A;
Andrew Granville
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On the Brahmagupta-Fermat-Pell Equation: The Chakravāla or Cyclic algorithm revisited
, 2023 In the following pages we take a fresh look at the ancient Indian Chakravāla or Cyclic algorithm for solving the Brahmagupta-Fermat-Pell quadratic Diophantine equation in integers taking account of recent developments.
Mitter, Pronob
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Parametric solutions to the generalized Fermat equation
, 1999 In this paper we examine parametric solutions to the generalized Fermat equation, xp+yq=zr. Simple criteria are given for the existence of solutions over an algebraically closed field and all such solutions are described.
Esmonde, Jody.
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Parity Properties of Equations, Related to Fermat Last Theorem
, 2019 A possibility of elementary proof of Fermat Last Theorem (FLT) on the basis of parity considerations is considered. FLT was formulated by Fermat in 1637, and proved by A. Wiles in 1995. Here, a simpler approach is considered. The idea is to subdivide the
Shestopaloff Yuri K. +1 more
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A modular approach to Fermat equations of signature $(p,p,5)$ using Frey hyperelliptic curves
, 2022 In this paper we carry out the steps of Darmon's program for the generalized Fermat equation $$ x^p + y^p = z^5. $$ In particular, we develop the machinery necessary to prove an optimal bound on the exponent $p$ for solutions satisfying certain $2$-adic ...
Koutsianas, Angelos, Chen, Imin
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A Factorial Power Variation of Fermat\u27s Equation
, 2017 We consider a variant of Fermat\u27s well-known equation xn+yn=zn. T his variant replaces the usual powers with the factorial powers defined by xn=x(x-1)...(x-(n-1)). For n=2 we characterize all possible integer solutions of the equation. For n=3 we
Green, Matthew J.
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On solutions of several Fermat-type partial differential-difference equations in C2
Demonstratio MathematicaIn this paper, we study entire solutions of several Fermat-type partial differential-difference equations in C2 ${\mathbb{C}}^{2}$ by applying Nevanlinna theory of meromorphic functions in several complex variables.
Tang Caoqiang, Huang Zhigang
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Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0
, 2011 Let C: y(2)=f(x) be a hyperelliptic curve defined over Q. Let K be a number field and suppose f factors over K as a product of irreducible polynomials f=f(1) f(2) ... f(r).
Michael Stoll +3 more
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The proof of Fermat\u27s last theorem
, 2000 Fermat, Pierre de, is perhaps the most famous number theorist who ever lived. Fermat\u27s Last Theorem states that the equation xn + yn = zn has no non-zero integer solutions for x, y and z when n ...
Trad, Mohamad
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On Darmon's program for the generalized Fermat equation, I
In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of $\mathrm{GL}_2$-type over totally real fields. The original approach was based on hard open conjectures, which have made it difficult to
Freitas, N. +9 more
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