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Bertrand’s postulate

Andrijana Ćurković   ORCID icon orcid.org/0000-0003-2340-5767 ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu
Borka Jadrijević   ORCID icon orcid.org/0000-0002-5913-3719 ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu
Marina Simić ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu

Puni tekst: hrvatski, pdf (404 KB) str. 139-150 preuzimanja: 151* citiraj
APA 6th Edition
Ćurković, A., Jadrijević, B. i Simić, M. (2017). Bertrandov postulat. Osječki matematički list, 17 (2), 139-150. Preuzeto s https://hrcak.srce.hr/193190
MLA 8th Edition
Ćurković, Andrijana, et al. "Bertrandov postulat." Osječki matematički list, vol. 17, br. 2, 2017, str. 139-150. https://hrcak.srce.hr/193190. Citirano 13.11.2019.
Chicago 17th Edition
Ćurković, Andrijana, Borka Jadrijević i Marina Simić. "Bertrandov postulat." Osječki matematički list 17, br. 2 (2017): 139-150. https://hrcak.srce.hr/193190
Harvard
Ćurković, A., Jadrijević, B., i Simić, M. (2017). 'Bertrandov postulat', Osječki matematički list, 17(2), str. 139-150. Preuzeto s: https://hrcak.srce.hr/193190 (Datum pristupa: 13.11.2019.)
Vancouver
Ćurković A, Jadrijević B, Simić M. Bertrandov postulat. Osječki matematički list [Internet]. 2017 [pristupljeno 13.11.2019.];17(2):139-150. Dostupno na: https://hrcak.srce.hr/193190
IEEE
A. Ćurković, B. Jadrijević i M. Simić, "Bertrandov postulat", Osječki matematički list, vol.17, br. 2, str. 139-150, 2017. [Online]. Dostupno na: https://hrcak.srce.hr/193190. [Citirano: 13.11.2019.]

Sažetak
Joseph Bertrand, in 1845, conjectured that for all positive integers
n there exists a prime number between n and 2n. This statement is
known as Bertrand’s postulate. Bertrand verified his conjecture for n <
3 · 10^6, but he did not prove it. The conjecture was proved in 1850 by
Pafnuty Cherbyshev. In this paper we present the proof published by
Paul Erdös in his first article in 1932. The proof is elementary and uses
only a few simple properties of binomial coefficients. In addition, we
will see how Bertrand’s postulate is related to some famous assertions
and conjectures concerning prime numbers.

Ključne riječi
Bertrand’s postulate; prime numbers; binomial coefficient; Prime Number Theorem; Goldbach’s conjecture

Hrčak ID: 193190

URI
https://hrcak.srce.hr/193190

[hrvatski]

Posjeta: 401 *