Skip to main content

Elementary Number Theory Problems. Part XIX Cover

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

Elementary Number Theory Problems. Part XIX

Formalized Mathematics

Volume 33 (2025): Issue 1 (September 2025)

By: Karol Pąk

Open Access

|Dec 2025

Abstract

In this paper, we present formal solutions to twelve problems selected from Wacław Sierpiński’s book 250 Problems in Elementary Number Theory. The selected problems are: 108, 112–114, 118–119, 127, 129, 130, and 132–134 formalized in the Mizar system.

References

P.T. Bateman, J.L. Selfridge, and S.S. Wagsta Jr. The editor’s corner: The new Mersenne conjecture. The American Mathematical Monthly, 96(2):125–128, 1989. doi:10.1080/00029890.1989.11972155.
Search in Google Scholar Back to article
Mario Carneiro. The divergence of the sum of prime reciprocals. Formalized Mathematics, 30(3):209–210, 2022. doi:10.2478/forma-2022-0015.
Search in Google Scholar Back to article
John Horton Conway and R.K. Guy. The Book of Numbers. Springer-Verlag, 1996.
Search in Google Scholar Back to article
G. Di Pietro. New estimations for numerical analysis approach to twin primes conjecture. Notes on Number Theory and Discrete Mathematics, 30(3):580–586, 2024. doi:10.7546/nntdm.2024.30.3.580-586.
Search in Google Scholar Back to article
Leonard Eugene Dickson. History of Theory of Numbers. New York, 1952.
Search in Google Scholar Back to article
Harvey Dubner and Wilfrid Keller. Factors of generalized Fermat numbers. Mathematics of Computation, 64(209):397–405, 1995. doi:10.2307/2153343.
Search in Google Scholar Back to article
Richard K. Guy. Unsolved Problems in Number Theory. Problem Books in Mathematics. Springer, third edition, 2004. doi:10.1007/978-0-387-26677-0.
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. Elementary number theory problems. Part XIV – Diophantine equations. Formalized Mathematics, 32(1):47–63, 2024. doi:10.2478/forma-2024-0004.
Search in Google Scholar Back to article
Michal Křížek, Florian Luca, and Lawrence Somer. Factors of Fermat numbers. In 17 Lectures on Fermat Numbers: From Number Theory to Geometry, pages 70–79. Springer New York, 2001. doi:10.1007/978-0-387-21850-27.
Search in Google Scholar Back to article
Louis J. Mordell. Diophantine Equations. Academic Press, 1969.
Search in Google Scholar Back to article
Adam Naumowicz. Elementary number theory problems. Part I. Formalized Mathematics, 28(1):115–120, 2020. doi:10.2478/forma-2020-0010.
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:10.1007/978-3-030-53518-622.
Search in Google Scholar Back to article
Karol Pąk. Elementary number theory problems. Part XVI. Formalized Mathematics, 32 (1):203–212, 2024. doi:10.2478/forma-2024-0017.
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. Teoria liczb. Instytut Matematyczny Polskiej Akademii Nauk, 1950. In Polish.
Search in Google Scholar Back to article
Wacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/forma-2025-0020 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

Journal RSS Feed

Language: English

Page range: 245 - 265

Submitted on: Dec 17, 2025

|

Accepted on: Dec 21, 2025

|

Published on: Dec 31, 2025

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Related subjects:

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2025 Karol Pąk, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 33 (2025): Issue 1 (September 2025)

Previous article