Download
PDF 273.74 KB
master's thesis
36   13
High order congruences
Jelena Lalić (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Metadata
TitleKongruencije višeg reda
AuthorJelena Lalić
Mentor(s)Ivan Matić (thesis advisor)
Abstract
U ovom radu upoznat ćemo se s metodama određivanja uvijeta za egzistenciju rješenja polinomijalnih kongruencija te pronalaženja istih. Glavni dio rada podijeljen je u pet poglavlja,od kojih prva dva daju dovoljno temeljnog znanja o djeljivosti i kongruencijama te njihovim svojstvima. Također su promatrane linearne kongruencije kao i rješavanje sustava linearnih kongruencija koristeći Kineski teorem o ostacima. U četvrtom poglavlju posebna paznjaje usmjerena na kvadratne kongruencije. Definiran je pojam Legendreovog simbola te supredstavljeni rezultati koji vode lakšem određivanju njegove vrijednosti. Svi teorijski rezultatiu radu primjenjeni su na konkretnim primjerima. U posljednjem poglavlju ćemo preko definicije reda prirodnog broja a modulo n doći do pojma primitivnog korijena modulo n.Pokazat ćemo kako odrediti je li neki prirodni broj primitivan korijen modulo n. Spomenuti pojam bit ce ključan u rješavanju polinomijalnih kongruencija.
Keywordspolynomial congruence modulo Legendre symbol Jacobi symbol primitiveroot
Parallel title (English)High order congruences
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Pure Mathematics
Algebra and Calculus Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Study programme typeuniversity
Study levelintegrated undergraduate and graduate
Study programmeMathematics and Computer Science
Academic title abbreviationmag. educ. math. et inf.
Genremaster's thesis
Language Croatian
Defense date2016-12
Parallel abstract (English)
In this paper we will introduce the methods of determining the conditions for the existence ofsolutions of polynomial congruence and technique to obtain such solutions. The main part ofthis paper is divided into five chapters, of which the first two provide enough basic knowledgeabout the divisibility and congruence and their properties. We study a linear congruence andsolving systems of linear congruences using the Chinese theorem of residues. In the fourthchapter, special attention is focused on quadratic congruence. We define Legendre symboland presents the results which lead to easier determine its value. All theoretical results inthe work were applied to particular examples. In the last chapter we introduce the conceptof the order of integer modulo n and then we define primitive roots modulo n and show howto determine whether an integer is primitive modulo n or not. The mentioned term will bea key to solving polynomial congruence.
Parallel keywords (Croatian)polinomijalna kongruencija modulo Legendreov simbol Jacobijev simbol primitvni korijen
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:694694