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undergraduate thesis
On Consecutive Palindromes
2020. urn:nbn:hr:126:318353
Veselovac, Matej
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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Veselovac, M. (2020). On Consecutive Palindromes (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:318353

Veselovac, Matej. "On Consecutive Palindromes." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:318353

Veselovac, Matej. "On Consecutive Palindromes." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:318353

Veselovac, M. (2020). 'On Consecutive Palindromes', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 17 November 2023, https://urn.nsk.hr/urn:nbn:hr:126:318353

Veselovac M. On Consecutive Palindromes [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2023 November 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:318353

M. Veselovac, "On Consecutive Palindromes", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:318353

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Metadata
TitleOn Consecutive Palindromes
Title (croatian)O uzastopnim palidromima
AuthorMatej Veselovac
MentorIvan Soldo (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 country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
In this paper, we will try to characterize consecutive palindromes - positive integers simultaneously palindromic in multiple consecutive number bases. We search for solutions in the cases of two and three number bases and observe the fact that solutions likely do not exist in the case of four or more number bases. In practice, this requires solving systems of corresponding linear Diophantine equations. This was motivated by the question Can a positive integer be palindromic in more than three consecutive number bases?. The question does not appear to have an obvious approach and remains open. The analysis of consecutive palindromes in three number bases suggests that the answer to the question is likely negative.
Abstract (english)
U ovom radu pokušatćemo karakterizirati uzastopne palindrome - brojeve koji su istovremeno palindromčni u všestruko uzastopnih brojevnih baza. Tržimo rješenja u slučajevima dvije i tri brojevne baze, te promatramo činjenicu kako rješenja vjerojatno ne postoje u slučaju četiri ili više brojevnih baza. U praksi, ovo zahtjeva rješavanje sustava odgovarajućih linearnih Diofantskih jednadžbi. Ovaj rad je motiviralo pitanje Može li broj biti palindromičan u više od tri uzastopne brojevne baze? Čini se kako pitanje nema očit pristup te ostaje otvoreno. Analiza uzastopnih palindroma u tri brojevne baze upućuje nas na to da bi odgovor na postavljeno pitanje bio negativan.
Keywords
Keywords (english)
Languageenglish
URN:NBNurn:nbn:hr:126:318353
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 on2020-12-15 08:33:04