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master's thesis
Savršeni i Mersenneovi brojevi
2019. urn:nbn:hr:126:517555
Patković, Kristina
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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Patković, K. (2019). Savršeni i Mersenneovi brojevi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:517555

Patković, Kristina. "Savršeni i Mersenneovi brojevi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:517555

Patković, Kristina. "Savršeni i Mersenneovi brojevi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:517555

Patković, K. (2019). 'Savršeni i Mersenneovi brojevi', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 20 October 2024, https://urn.nsk.hr/urn:nbn:hr:126:517555

Patković K. Savršeni i Mersenneovi brojevi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 October 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:517555

K. Patković, "Savršeni i Mersenneovi brojevi", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:517555

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Metadata
TitleSavršeni i Mersenneovi brojevi
Title (english)Perfect and Mersenne Numbers
AuthorKristina Patković
MentorIvan Matić (mentor)
Committee memberTomislav Marošević (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberMihaela Ribičić Penava (član povjerenstva)
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 country2019-10-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu proučavamo Mersenneove i savršene brojeve. Kažemo da je prirodan broj N savršen ako je σ(N) = 2N, gdje je σ(N) suma pravih djelitelja broja N. Poznato je da je broj oblika \( 2^{p-1}( 2^{p}-1 )\) , gdje je \(2^{p-1}\) prost, paran savršen broj. Svi dosad poznati savšeni brojevi su parni. Nije poznato postoje li ili ne neparni savršeni brojevi, ali pronađeni su mnogi uvjeti koje bi trebali zadovoljavati u slučaju postojanja. Mersenneov broj jest broj oblika \( M_{n}=2^{n}-1\), a Mersenneov prost broj je Mersenneov broj koji je prost. Postoje različite metode kojima se testira prostost Mersenneovih brojeva. Vrlo učinkovit test prostosti jest Lucas-Lehmerov test.
Abstract (english)
In this paper we study Mersenne numbers and perfect numbers. We say that natural number N is perfect if σ(N) = 2N, where σ(N) denotes the sum of the positive divisors of N. It is well known that a number is even and perfect if and only if it has the form \( 2^{p-1} ( 2^{p}-1 )\) where \(2^{p-1}\) is prime. All presently known perfect numbers are even. It is unknown whether or not odd perfect numbers exist, although many conditions necessary for their existance have been found. A number of the form \( M_{n}=2^{n}-1\) called Mersenne number, and Mersenne number which is prime is called Mersenne prime. There are various methods for testing the primality of Mersenne numbers. Lucas-Lehmer test is an extremely efficient primality test for Mersenne primes.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:517555
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-10-28 09:31:23