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undergraduate thesis
Kineski teorem o ostatcima
2019. urn:nbn:hr:126:258546
Tobijas, Tomislav
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Tobijas, T. (2019). Kineski teorem o ostatcima (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:258546

Tobijas, Tomislav. "Kineski teorem o ostatcima." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:258546

Tobijas, Tomislav. "Kineski teorem o ostatcima." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:258546

Tobijas, T. (2019). 'Kineski teorem o ostatcima', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 15 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:258546

Tobijas T. Kineski teorem o ostatcima [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2025 January 15] Available at: https://urn.nsk.hr/urn:nbn:hr:126:258546

T. Tobijas, "Kineski teorem o ostatcima", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:258546

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Metadata
TitleKineski teorem o ostatcima
Title (english)Chinese Remainder Theorem
AuthorTomislav Tobijas
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2019-09-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom završnom radu prisjetili smo se definicije kongruencija te smo kroz razne primjere prošli kroz par realističnih primjena kongruencija. Nadalje, upoznali smo i sustave od dvije i više kongruencija u kojima smo promatrali specifične oblike kongruencija od kojih je jedan i Kineski teorem o ostacima. Osvrnuli smo se i na druge metode rješavanja sustava koje koriste posebne, dodatne sustave kao pomoć pri rješavanju početnog zadanog sustava kongruencija. Sve metode navedene u ovom završnom radu imaju podudaranja u dijelovima načina rješavanja te se većina ovih metoda koristila u starim civilizacijama kao promoć pri računanju zahtjevnijih i kompliciranijih zadataka i problema. Također, dotaknuli smo se i primjena kongruencija u kriptografiji te mogućnosti korištenja istih pri raznim šifriranjima i dešifriranjima podataka. Naposlijetku dotaknuli smo se i algebarskih prstena te homomorfizama prstena u kojima se pri dokazu određenih teorema i propozicija između ostaloga koristi i Kineski teorem o ostacima.
Abstract (english)
In this paper, we recalled the definition of congruences and we presented a couple of examples which show few realistic applications of congruences. Furthermore, we introduced systems of two or more congruences in which we were looking at specific forms of congruences of which one method of solving given system is known as the Chinese Remainder Theorem. We also looked at other solution methods which use special additional systems which serve as help for solving the original given system of congruences. All solving methods that are named in this paper have some similarities in the way they solve certain systems of congruences and also, most of these methods were used in ancient civilizations as a help in solving more demanding and more complicated tasks and problems. Also, we mentioned few applications of congruences in cryptography and the possibility of using them in different encriptions and decriptions of data. In the end, we’ve talked about algebraic rings and ring homomorphisms which use Chinese Remained Theorem for proving certain theorems and propositions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:258546
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
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Created on2019-09-13 10:42:42