Elementary Number Theory Problems. Part VIII

Artur Korniłowicz

doi:10.2478/forma-2023-0009

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

Elementary Number Theory Problems. Part VIII

Formalized Mathematics

Volume 31 (2023): Issue 1 (September 2023)

By: Artur Korniłowicz

Open Access

|Oct 2023

Abstract

In this paper problems 25, 86, 88, 105, 111, 137–142, and 184–185 from [12] are formalized, using the Mizar formalism [3], [1], [4]. This is a continuation of the work from [5], [6], and [2] as suggested in [8]. The automatization of selected lemmas from [11] proven in this paper as proposed in [9] could be an interesting future work.

References

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.
Search in Google Scholar Back to article
Adam Grabowski. Elementary number theory problems. Part VI. Formalized Mathematics, 30(3):235–244, 2022. doi:10.2478/forma-2022-0019.
Search in Google Scholar Back to article
Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.
Search in Google Scholar Back to article
Artur Korniłowicz. Flexary connectives in Mizar. Computer Languages, Systems & Structures, 44:238–250, December 2015. doi:10.1016/j.cl.2015.07.002.
Search in Google Scholar Back to article
Artur Korniłowicz. Elementary number theory problems. Part IV. Formalized Mathematics, 30(3):223–228, 2022. doi:10.2478/forma-2022-0017.
Search in Google Scholar Back to article
Artur Korniłowicz and Adam Naumowicz. Elementary number theory problems. Part V. Formalized Mathematics, 30(3):229–234, 2022. doi:10.2478/forma-2022-0018.
Search in Google Scholar Back to article
Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179–186, 2004.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Adam Naumowicz. Extending numeric automation for number theory formalizations in Mizar. In Catherine Dubois and Manfred Kerber, editors, Intelligent Computer Mathematics – 16th International Conference, CICM 2023, Cambridge, UK, September 5–8, 2023, Proceedings, volume 14101 of Lecture Notes in Computer Science, pages 309–314. Springer, 2023. doi:10.1007/978-3-031-42753-4 23.
Search in Google Scholar Back to article
Marco Riccardi. Solution of cubic and quartic equations. Formalized Mathematics, 17(2): 117–122, 2009. doi:10.2478/v10037-009-0012-z.
Search in Google Scholar Back to article
Wacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964.
Search in Google Scholar Back to article
Wacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.
Search in Google Scholar Back to article