Search results for "Fermat"
showing 10 items of 16 documents
Alkulukutesteistä
2016
Tämän tutkielman tavoitteena on esittää tunnetuimmat alkulukutestit niin matemaattiselta perustoiltaan kuin käytännön toteutuksiltaan ohjelmakoodin muodossa. Alkulukutestit jaotellaan yleisesti deterministisiin ja probabilistisiin testeihin; deterministiset testit antavat täysin varman vastauksen, mutta ovat suurille luvuille huomattavasti probabilistia testejä hitaampia. Probabilistiset testit ovat nopeita tehdä, mutta saattavat antaa väärän vastauksen. Testien suoritusaikaa mitataan karkeasti niiden suorittamiseksi vaadittavien laskutoimitusten lukumääarällä. Tutkielmassa käsitellään deterministisistä testeistä jakolaskumenetelmä, Wilsonin lause, Prothin testi, Lucasin ja Lehmerin testi j…
Poincaré Week in Göttingen, 22–28 April 1909
2018
When Paul Wolfskehl died in 1906, his will established a prize for the first mathematician who could supply a proof of Fermat’s Last Theorem, or give a counterexample refuting it. The interest from this prize money was later used to bring world-renowned mathematicians to Gottingen to deliver a series of lectures. Hilbert was apparently very pleased with this arrangement, and once jested that the only thing that kept him from proving Fermat’s famous conjecture was the thought of killing the goose that laid these golden eggs.
Valutare la devianza costruttiva nei contesti di lavoro
2017
Il presente lavoro fornisce un contributo al tema della devianza organizzativa costruttiva, intesa come un insieme di comportamenti volontari di violazione delle norme organizzative e delle procedure di lavoro, con l’intento di rispondere efficacemente ai problemi organizzativi e finalizzati a conseguire una buona performance. Attraverso due studi indipendenti è stato proposto un adattamento italiano della scala di devianza organizzativa costruttiva (Galperin, 2012), che ha mostrato, tramite analisi esplorative e confermative, soddisfacenti risultati dal punto di vista psicometrico e della validità convergente e discriminante. Sono emerse inoltre le relazioni positive del costrutto con il p…
Fermat quotient and the p-th root of a p-adic integer
2008
Fermat'n pieni lause
2009
Tässä työssä tutkimme Fermat’n pientä lausetta, Eulerin funktiota ja yksiköiden ryhmää. Toteamme myös, että on olemassa lukuja, jotka toteuttavat Fermat’n lauseen kaavan olematta kuitenkaan alkulukuja. Todistamme lisäksi Fermat’n lausetta yleisemmän tuloksen. Lopuksi perehdymme hieman Eulerin ja Fermat’n lauseiden sovelluksiin salausmenetelmissä.
Quotients of Fermat curves and a Hecke character
2005
AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.
Quotients of Hypersurfaces in Weighted Projective Space
2009
Abstract In [Bini, van Geemen, Kelly, Mirror quintics, discrete symmetries and Shioda maps, 2009] some quotients of one-parameter families of Calabi–Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let A be an invertible matrix with non-negative integer entries. We introduce varieties XA and in weighted projective space and in , respectively. The variety turns out to be a quotient of a Fermat variety by a finite group. As a by-product, XA is a quotient of a Fermat variety and is a quotient of XA by a finite group. We apply this construction to som…
On Pareto optima, the Fermat-Weber problem, and polyhedral gauges
1990
This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ℝn. It emphasizes the case in which the gauges are polyhedral. In this framework the following result is known: if the gauges are polyhedral, then each Pareto optimum is the solution to a Fermat—Weber problem with strictly positive coefficients. We give a new proof of this result, and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges. Also, we characterize polyhedral gauges in terms of a property of their subdifferential.
Symmetries and equations of smooth quartic surfaces with many lines
2017
We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.