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master's thesis
Primjena kongruencija
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. urn:nbn:hr:126:114640
Užar, Irena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Užar, I. (2016). Primjena kongruencija (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:114640

Užar, Irena. "Primjena kongruencija." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:114640

Užar, Irena. "Primjena kongruencija." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:114640

Užar, I. (2016). 'Primjena kongruencija', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:114640

Užar I. Primjena kongruencija [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 December 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:114640

I. Užar, "Primjena kongruencija", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:114640

Metadata
TitlePrimjena kongruencija
Title (english)Congruence Applications
AuthorIrena Užar
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 country2016-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U diplomskom radu pokazat ćemo kako se kongruencija može primjeniti na različite načine. Prvo ćemo definirati kongruenciju i navesti njezina svojstva koja ćemo koristiti u radu. Zatim ćemo prikazati neke od njezinih primjena. Prvo neke od jednostavnjih poput testa djeljivosti za brojeve 10, 5, 2^{i}, 3 , 9 i 11 koje se dokazuju primjenom kongruencija, zatim metoda odbacivanja devetki i digitalni korijen. Nakon toga ćemo vidjeti kako se kongruencija koristi za modeliranje dizajna, preko zvijezde s m vrhova, (m, n) dizajna ostataka do quilt dizajna. Zatim slijede primjene koje omugućavaju otkrivanje grešaka u identifikacijskim brojevima (UPC, EAN-13, ISBN,...). I na kraju ćemo prikazati kako se primjenom kongruencija može rješiti problem p-kraljica, raspored timova po skupinama (round-robin turnir) te odredivanje dana u tjednu za bilo koji datum i bilo koju godinu (Perpetual kalendar).
Abstract (english)
In this work we will show how congruence has applications on many different ways. First we will define congruence and show it properties that we will use in work. Then we will show some simple applications like divisibility test for numbers 10, 5, 2^{i}, 3 , 9 and 11, prove them with congruence. Then we will show method casting out nines and digital roots. After that we will see how congruence is applied on design modular designs, from m-pointed star, (m, n) residue design to quilt design. In third part we will show how congruence is used to detect mistakes in identification numbers (UPC, EAN-13, ISBN,...) In the final three parts we will show how congruence applications can help to solve the pQueens Puzzle, Round-Robin tournaments and to determinate the day of the week for any date and any year.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:114640
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2016-11-29 08:54:09