Elementary Number Theory Problems. Part XIV – Diophantine Equations
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.
- Edward J. Barbeau. Pell’s Equation. Problem Books in Mathematics. Springer, 2003.
- Robert D. Carmichael. Diophantine Analysis. New York, John Wiley & Sons, 1915.
- Adam Grabowski. Elementary number theory problems. Part XII – primes in arithmetic progression. Formalized Mathematics, 31(1):277–286, 2023. doi:10.2478/forma-2023-0022.
- Adam Grabowski and Christoph Schwarzweller. Revisions as an essential tool to maintain mathematical repositories. In M. Kauers, M. Kerber, R. Miner, and W. Windsteiger, editors, Towards Mechanized Mathematical Assistants. Lecture Notes in Computer Science, volume 4573, pages 235–249. Springer: Berlin, Heidelberg, 2007.
- 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.
- Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4): 573–577, 1997.
- Artur Korniłowicz. Elementary number theory problems. Part IX. Formalized Mathematics, 31(1):161–169, 2023. doi:10.2478/forma-2023-0015.
- Artur Korniłowicz and Adam Naumowicz. Elementary number theory problems. Part V. Formalized Mathematics, 30(3):229–234, 2022. doi:10.2478/forma-2022-0018.
- Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179–186, 2004.
- 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.
- Andrzej Schinzel. Démonstration d’une conséquence de l’hypothèse de Goldbach. Compositio Mathematica, 14:74–76, 1959.
- Andrzej Schinzel and Wacław Sierpiński. Sur certaines hypothèses concernant les nombres premiers. Acta Arithmetica, 4(3):185–208, 1958.
- Christoph Schwarzweller. Modular integer arithmetic. Formalized Mathematics, 16(3): 247–252, 2008. doi:10.2478/v10037-008-0029-8.
- Wacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964.
- Wacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.
- Wacław Sierpiński. Remarques sur le travail de M. J. W. S. Cassels «On a diophantine equation». Acta Arithmetica, 6(4):469–471, 1961.
- Li Yan, Xiquan Liang, and Junjie Zhao. Gauss lemma and law of quadratic reciprocity. Formalized Mathematics, 16(1):23–28, 2008. doi:10.2478/v10037-008-0004-4.
Language: English
Page range: 47 - 63
Accepted on: Oct 22, 2024
Published on: Nov 26, 2024
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2024 Artur Korniłowicz, published by University of Białystok
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