Elementary Number Theory Problems. Part VI

Adam Grabowski

doi:10.2478/forma-2022-0019

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Elementary Number Theory Problems. Part VI

Formalized Mathematics

Volume 30 (2022): Issue 3 (October 2022)

By: Adam Grabowski

Open Access

|Dec 2022

Abstract

This paper reports on the formalization in Mizar system [1], [2] of ten selected problems from W. Sierpinski’s book “250 Problems in Elementary Number Theory” [7] (see [6] for details of this concrete dataset). This article is devoted mainly to arithmetic progressions: problems 52, 54, 55, 56, 60, 64, 70, 71, and 73 belong to the chapter “Arithmetic Progressions”, and problem 50 is from “Relatively Prime Numbers”.

References

[1] Grzegorz Bancerek, Czesław Bylinacute;ski, 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.
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[2] Grzegorz Bancerek, Czesław Bylinacute;ski, 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
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[3] Adam Grabowski. On square-free numbers. Formalized Mathematics, 21(2):153–162, 2013. doi:10.2478/forma-2013-0017.
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[4] Adam Grabowski. Polygonal numbers. Formalized Mathematics, 21(2):103–113, 2013. doi:10.2478/forma-2013-0012.
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[5] Magdalena Jastrz¸ebska and Adam Grabowski. Some properties of Fibonacci numbers. Formalized Mathematics, 12(3):307–313, 2004.
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[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.
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[7] Wacław Sierpinacute;ski. 250 Problems in Elementary Number Theory. Elsevier, 1970.
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