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undergraduate thesis
Kongruencije i neke njihove primjene
2021. urn:nbn:hr:126:186888
Radaković, Maja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Radaković, M. (2021). Kongruencije i neke njihove primjene (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:186888

Radaković, Maja. "Kongruencije i neke njihove primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:186888

Radaković, Maja. "Kongruencije i neke njihove primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:186888

Radaković, M. (2021). 'Kongruencije i neke njihove primjene', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 18 April 2024, https://urn.nsk.hr/urn:nbn:hr:126:186888

Radaković M. Kongruencije i neke njihove primjene [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 April 18] Available at: https://urn.nsk.hr/urn:nbn:hr:126:186888

M. Radaković, "Kongruencije i neke njihove primjene", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:186888

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Metadata
TitleKongruencije i neke njihove primjene
Title (english)Congruences and Some of Their Applications
AuthorMaja Radaković
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Ovim završnim radom obradit će se tema kongruencija i nekih njihovih primjena. Teorija kongruencija uvedena je u djelu njemačkog matematičara Carla Friedricha Gaussa pod nazivom Disquisitiones Arithmeticae. Uveo je oznaku za kongruencije koju koristimo i danas. U uvodu ćemo denirati kongruencije te navesti neke primjere i osnovna svojstva. U prvom poglavlju osvrnut ćemo se na linearne kongruencije te navesti neke njihove primjene. U drugom poglavlju iskazat ćemo i dokazati Kineski teorem o ostatcima te detaljnije opisati sustave kongruencija i njihove primjene. U trećem poglavlju bazirat ćemo se na Eulerovu funkciju i njena svojstva te iskazati i dokazati Euler-Fermatov teorem i upoznati se s reduciranim sustavom ostataka. Nadalje, u četvrtom poglavlju proučit ćemo kongruencije po prostom modulu te iskazati i dokazati Wilsonov i Lagrangeov teorem. Naposljetku, u petom poglavlju vidjet ćemo neke primjene kongruencija u kriptografji, ispitivanju djeljivosti i u generiranju barkodova proizvoda.
Abstract (english)
In this nal paper, we will analyze congruences and some of their applications. The theory of congruence was introduced by the German mathematician Carl Friedrich Gauss in his work Disquisitiones Arithmeticae. He introduced the congruence sign that we still use. In the introduction, we will dene congruences and give some examples and basic properties. In the rst chapter, we will consider linear congruences and some of their applications. In the second chapter, we will state and prove the Chinese theorem of residues and in more detail describe the systems of congruences and their applications. The theme of the next chapter will be Euler's function and its properties. We will also state and prove the EulerFermat theorem, and consider the reduced system of residues. Furthermore, in the fourth chapter, we will study congruences by a simple module, express and prove Wilson's and Lagrange's theorem. Finally, in chapter ve, we will see some of applications of congrunces in cryptography, divisibility testing and in generating product barcodes.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:186888
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-11-09 07:14:24