Results 1 to 10 of about 83 (79)

Laws of Reciprocity and the First Case of Fermat's Last Theorem. [PDF]

Proc Natl Acad Sci U S A, 1925
Vandiver HS.
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The first case of fermat’s last theorem

The Mathematical Intelligencer, 1985
The author surveys his proof with \textit{L. M. Adleman} and \textit{E. Fouvry} contained in the union of the two papers [Invent. Math. 79, 409-416 (1985; Zbl 0557.10034), ibid. 79, 383-407 (1985; Zbl 0557.10035)] that the ''First Case'' of Fermat's equation \(x^ p+y^ p=z^ p\); \(p\nmid xyz\) has, for infinitely many primes p, no solutions in natural ...
Heath-Brown, D.R., Adleman, L.M.
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A New Criterion for the First Case of Fermat's Last Theorem [PDF]

Mathematics of Computation, 1995
It is shown that if the first case of Fermat’s last theorem fails for an odd prime l , then the sums of reciprocals modulo l , s
Dilcher, Karl, Skula, Ladislav
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SPECIAL COURSE FOR SCHOOLCHILDREN: PROOF OF FERMAT'S GREAT THEOREM BY EXAMPLE x^3+y^3+z^3=0 [PDF]

Vestnik Issyk-Kulʹskogo universiteta
It is difficult to find a person among mathematicians who is not familiar with and does not study the solution of the equation x^2+y^2+z^2=0, or x^3+y^3+z^3=0 in integers.
Srashidinov A.
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New bound for the first case of Fermat’s last theorem [PDF]

Mathematics of Computation, 1989
We present an improvement to Gunderson’s function, which gives a lower bound for the exponent in a possible counterexample to the first case of Fermat’s "Last Theorem," assuming that the generalized Wieferich criterion is valid for the first n prime bases. The new function increases beyond n = 29 n = 29 , unlike
Jonathan W. Tanner, Samuel S. Wagstaff
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On congruences related to the first case of Fermat’s last theorem [PDF]

Mathematics of Computation, 1977
Solutions to the congruences ( 1 + a
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The First Case of Fermat's Last Theorem is True for all Prime Exponents up to 714,591,416,091,389 [PDF]

Transactions of the American Mathematical Society, 1988
We show that if the first case of Fermat’s Last Theorem is false for prime exponent p p then
Granville, Andrew, Monagan, Michael B.
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On Krasnér's theorem for the first case of Fermat's last theorem [PDF]

Colloquium Mathematicum, 1994
The solvability of the Fermat equation \(x^ p + y^ p = z^ p\) \((p\) an odd prime) in the so-called first case would imply that \(p\) divides the Bernoulli numbers \(B_{p-n-1}\) for all \(n\) up to \(k(p) = 2[(\log p)^{1/3}]\). This is the content of M. Krasner's classical theorem supplemented by a computational result.
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On the first case of fermat's last theorem, II

Manuscripta Mathematica, 1986
Let \(p\) be an odd prime and consider the equation (*) \(x^p + y^p + z^p = 0\) in the first case (i.e., \(p\nmid xyz)\), where \(x, y, z\) are nonzero integers prime to each other. As the criterion of (*) in the first case, it is well-known that the Kummer congruences \([d^{p-2}\{U_t(v)\}/dv^{p-2}]_{v=0}\equiv 0\pmod p\) and \(B_{2k}[d^{p-1- 2k}\{U_t ...
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An Observation on the First Case of Fermat's Last Theorem

Tokyo Journal of Mathematics, 1988
The main result of this paper is contained in the following Theorem: ``Let p be an odd prime and let x,y,z be integers with the properties \[ x^ p+y^ p+z^ p=0,\quad xyz\not\equiv 0 (mod p) \] (thus, the first case of Fermat's Last Theorem fails). Let M be an imaginary proper subfield of the cyclotomic field \(L={\mathbb{Q}}(\xi_ p)\). Put for \(T\in L:\
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