Elementary Number Theory Problems. Part III

Artur Korniłowicz

doi:10.2478/forma-2022-0011

.blurhash-client-img { display: none !important; }

Elementary Number Theory Problems. Part III

Formalized Mathematics

Volume 30 (2022): Issue 2 (July 2022)

By: Artur Korniłowicz

Open Access

|Dec 2022

Abstract

In this paper problems 11, 16, 19–24, 39, 44, 46, 74, 75, 77, 82, and 176 from [10] are formalized as described in [6], using the Mizar formalism [1], [2], [4]. Problems 11 and 16 from the book are formulated as several independent theorems. Problem 46 is formulated with a given example of required properties. Problem 77 is not formulated using triangles as in the book is.

References

[1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.
Open DOI Search in Google Scholar Back to article
[2] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.604425130069070
Open DOI Search in Google Scholar Back to article
[3] Adam Grabowski. Polygonal numbers. Formalized Mathematics, 21(2):103–113, 2013. doi:10.2478/forma-2013-0012.
Open DOI Search in Google Scholar Back to article
[4] Artur Korniłowicz. Flexary connectives in Mizar. Computer Languages, Systems & Structures, 44:238–250, December 2015. doi:10.1016/j.cl.2015.07.002.
Open DOI Search in Google Scholar Back to article
[5] Artur Korniłowicz and Dariusz Surowik. Elementary number theory problems. Part II. Formalized Mathematics, 29(1):63–68, 2021. doi:10.2478/forma-2021-0006.
Open DOI Search in Google Scholar Back to article
[6] Adam Naumowicz. Dataset description: Formalization of elementary number theory in Mizar. In Christoph Benzmüller and Bruce R. Miller, editors, Intelligent Computer Mathematics – 13th International Conference, CICM 2020, Bertinoro, Italy, July 26–31, 2020, Proceedings, volume 12236 of Lecture Notes in Computer Science, pages 303–308. Springer, 2020. doi:10.1007/978-3-030-53518-6_22.
Open DOI Search in Google Scholar Back to article
[7] Marco Riccardi. Solution of cubic and quartic equations. Formalized Mathematics, 17(2): 117–122, 2009. doi:10.2478/v10037-009-0012-z.
Open DOI Search in Google Scholar Back to article
[8] Christoph Schwarzweller. Modular integer arithmetic. Formalized Mathematics, 16(3): 247–252, 2008. doi:10.2478/v10037-008-0029-8.
Open DOI Search in Google Scholar Back to article
[9] Christoph Schwarzweller. Proth numbers. Formalized Mathematics, 22(2):111–118, 2014. doi:10.2478/forma-2014-0013.
Open DOI Search in Google Scholar Back to article
[10] Wacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.
Search in Google Scholar Back to article