Results 11 to 20 of about 142 (128)
On the first case of Fermat's last theorem
Journal of Number Theory, 1985 Suppose that there are integers a,b,c prime to each other and to p (an odd prime) such that \(a^ p+b^ p+c^ p=0\). Let \(u=-a/b\). Then, by a classical result, (*) \(B_ n\sum^{p-1}_{k=1}u^ k k^{-n}\equiv 0\) (mod p), where the \(B_ n\) are Bernoulli numbers \((n=0,...,p-2).\) The author gives a simple new expression and a simple proof for certain ...
Thaine, Francisco, Francisco Thaine
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On Krasner's Criteria for the First Case of Fermat's Last Theorem
Manuscripta Mathematica, 1986 The author uses an adaptation of Krasner's method [\textit{M. Krasner}, C. R. Acad. Sci., Paris 199, 256--258 (1934; Zbl 0010.00702)] to prove that if the first case of Fermat's last theorem is false for the prime \(p\), then \(p\) divides the numerator of the Bernoulli number \(B_{p-1-n}\) for all \(n\) between \(1\) and \([\sqrt{\log p/\log \log p}]\)
Andrew Granville
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Class Field Theory and the First Case of Fermat’s Last Theorem [PDF]
, 1997 For a prime number p, the first case of Fermat’s last theorem for exponent p asserts that for any three integers x, y, z with xp+yp+zp=O at least one of x, y, z is divisible by p. In the present chapter we use class field theory to prove several classical results concerning the first case.
Stevenhagen, P., Lenstra, H.W.
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An Elementary Proof of Fermat's Last Theorem v. 1.5
, 2023 In this present paper we will show you an elementary proof of the Fermat’s Last Theorem, that is ”too large to fit in the margin”, for the general case x^n + y^n = z^n .
Danilo Chavez (5827349)
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Diophantine equations after Fermat’s last theorem [PDF]
, 2009 The author considers the following two questions: {\parindent=7mm \item{(i)}Given a Diophantine equation, what information can be obtained by following the strategy of Wiles' proof of Fermat's last theorem?
Siksek, Samir, Samir Siksek
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On Fermat's last theorem and the Bernoulli numbers
, 1982 Using Kummer's criteria we show that if the first case of Fermat's last theorem fails for the prime p, then there exist irregular pairs satisfying certain ...
Agoh, Takashi
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Fermat's Last Theorem for regular primes
, 2023 We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}.
Birkbeck, Christopher +3 more
core
On Fermat's Last Theorem And The Arithmetic Of Z[ζp + ζp -1]
, 2015 Let p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A theorem, similar to Stickelberger's, is used to obtain certain relations involving a, b, and c.
Thaine F.
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Rational points on even‐dimensional Fermat cubics
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and ...
Alex Massarenti
wiley +1 more source
, 1982 We study properties of the polynomials φk(X) which appear in the formal development Πk − 0n (a + bXk)rk = Σk ≥ 0 φk(X) ar − kbk, where rk ∈ l and r = Σrk. this permits us to obtain the coefficients of all cyclotomic polynomials.
Thaine, F
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