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master's thesis
Wolstenholmeov teorem
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:354084
Jović, Lucija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Jović, L. (2019). Wolstenholmeov teorem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:354084

Jović, Lucija. "Wolstenholmeov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:354084

Jović, Lucija. "Wolstenholmeov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:354084

Jović, L. (2019). 'Wolstenholmeov teorem', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:354084

Jović L. Wolstenholmeov teorem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:354084

L. Jović, "Wolstenholmeov teorem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:354084

Metadata
TitleWolstenholmeov teorem
AuthorLucija Jović
MentorTomislav Pejković (mentor)
Committee memberTomislav Pejković (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Joseph Wolstenholme engleski je matematičar koji je 1862. godine dokazao da je za prost broj \(p\) veći od 3 brojnik racionalnog broja \(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\) djeljiv s \(p^{2}\). Ovaj diplomski rad posvećen je Wolstenholmeovom teoremu i sadrži četiri poglavlja. U prvom poglavlju izlažemo osnovne pojmove i rezultate iz teorije brojeva koji se koriste u nastavku rada. U drugom poglavlju iskazujemo i dokazujemo Wolstenholmeov teorem te navodimo tvrdnju ekvivalentnu navedenom teoremu. Treće poglavlje posvećeno je nekim generalizacijama Wolstenholmeovog teorema. Navedeno je i dokazano nekoliko varijacija, a zatim dokazana i generalizacija. U zadnjem poglavlju ovog rada pokazujemo kako obrat Wolstenholmeovog teorema vrijedi u određenim beskonačnim skupovima prirodnih brojeva.
Abstract (english)
Joseph Wolstenholme was an English mathematician who proved in 1862 that for a prime \(p\) greater than 3, the numerator of the fraction \(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\) is divisible by \(p^{2}\). This graduate thesis is devoted to the Wolstenohlme’s theorem and contains four chapters. In the first chapter, we give some of the fundamental terms and results from the theory of numbers used throughout the rest of the thesis. In the second chapter we state and prove Wolstenholme’s theorem and give an equivalent formulation. The third chapter gives some generalizations of Wolstenholme’s theorem. Several variations are stated and proved, followed by a generalization. In the last chapter of this graduate thesis, we prove that the converse of Wolstenholme’s theorem is true in certain infinite sets of natural numbers.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:354084
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-07-02 12:57:26