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undergraduate thesis
Kongruencije ili braća po ostatku
2022. urn:nbn:hr:179:220926
Mladina, Ivan
University of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
Department of Mathematics and Physics

Cite this document

Mladina, I. (2022). Kongruencije ili braća po ostatku (Undergraduate thesis). Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:179:220926

Mladina, Ivan. "Kongruencije ili braća po ostatku." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2022. https://urn.nsk.hr/urn:nbn:hr:179:220926

Mladina, Ivan. "Kongruencije ili braća po ostatku." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2022. https://urn.nsk.hr/urn:nbn:hr:179:220926

Mladina, I. (2022). 'Kongruencije ili braća po ostatku', Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, accessed 27 December 2024, https://urn.nsk.hr/urn:nbn:hr:179:220926

Mladina I. Kongruencije ili braća po ostatku [Undergraduate thesis]. Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture; 2022 [cited 2024 December 27] Available at: https://urn.nsk.hr/urn:nbn:hr:179:220926

I. Mladina, "Kongruencije ili braća po ostatku", Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:179:220926

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Metadata
TitleKongruencije ili braća po ostatku
AuthorIvan Mladina
MentorJosipa Barić (mentor)
GranterUniversity of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
(Department of Mathematics and Physics)
Split
Defense date and country2022-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
U ovom radu upoznajemo se s pojmom kongruencija po modulu i nekim njihovim osnovnim svojstvima. U prvom poglavlju definiramo bitne pojmove i teoreme vezane za djeljivost. U drugom poglavlju definiramo kongruencije po modulu, relacije, kao i relacije ekvivalencije, dokazujemo da je kongruencija po modulu relacija ekvivalencije na skupu cijelih brojeva, definiramo svojstva kongruencija modulo n na skupu cijelih brojeva, pokazujemo neke primjene kongruencija i pokazujemo kako se rješavaju sustavi kongruencija. Na kraju drugog poglavlja definiramo Eulerovu kongruenciju te Fermatov Mali stavak. U posljednjem poglavlju upoznajemo se sa kriptografijom te pokazujemo primjenu kongruencija u RSA kriptosustavu.
Abstract (english)
In this thesis we are introduced to congruences modulo n and some of their basic properties. In the first chapter we define important definitions and theorems related to divisibility rules. In the second chapter we define congruences modulo n, binary relation together with equivalence relation, we prove that congruence modulo n is an equivalence relation on the set of integers, we define properties of integer congruences modulo n, demonstrate some applications of congruences and show how to solve congruence systems. At the end of the second chapter we define Euler’s theorem and Fermat’s little theorem. In the last chapter we are introduced to cryptography and show some of the apllications of congruences in the RSA cryptosystem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:179:220926
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
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Created on2023-06-09 11:36:31