Pascal’s Triangle and Lucas’s Theorem

[1]Alif Anggoro, Eddy Liu, and Angus Tulloch. The Rascal triangle. The College Mathematics Journal, 41(5):393–395, 2010. doi:10.4169/074683410x521991.Open DOISearch in Google Scholar

[2]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 DOISearch in Google Scholar

[3]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.Open DOISearch in Google Scholar

[4]Alexis Bés. On Pascal triangles modulo a prime power. Annals of Pure and Applied Logic, 89(1):17–35, 1997. doi:10.1016/s0168-0072(97)85376-6.Open DOISearch in Google Scholar

[5]Chelsea Edmonds. Formalising combinatorial structures and proof techniques in Isabelle/HOL. Apollo – University of Cambridge Repository, 2023. doi:10.17863/CAM.108886.Open DOISearch in Google Scholar

[6]Chelsea Edmonds. Lucas’s theorem. Archive of Formal Proofs, 2020. https://isa-afp.org/entries/Lucas_Theorem.html, Formal proof development.Search in Google Scholar

[7]N.J. Fine. Binomial coefficients modulo a prime. The American Mathematical Monthly, 54(10):589–592, 1947. doi:10.2307/2304500.Open DOISearch in Google Scholar

[8]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.Open DOISearch in Google Scholar

[9]Andrew Granville. Arithmetic properties of binomial coefficients. I. Binomial coefficients modulo prime powers. In Jonathan M. Borwein, editor, Organic Mathematics: Proceedings of the Organic Mathematics Workshop, volume 20 of CMS conference proceedings, pages 253–276, Burnaby, BC, 1997. American Mathematical Soc. ISBN 9780821806685.Search in Google Scholar

[10]Artur Korniłowicz. Elementary number theory problems. Part IX. Formalized Mathematics, 31(1):161–169, 2023. doi:10.2478/forma-2023-0015.Open DOISearch in Google Scholar

[11]Włodzimierz Lapis. Dystynktywność ciągów. Investigationes Linguisticae, 25:58–71, 2012. doi:10.14746/il.2012.25.4.Open DOISearch in Google Scholar

[12]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 DOISearch in Google Scholar

[13]Karol Pąk. Prime representing polynomial with 10 unknowns. Formalized Mathematics, 30(4):255–279, 2022. doi:10.2478/forma-2022-0021.Open DOISearch in Google Scholar

[14]Christoph Schwarzweller. Modular integer arithmetic. Formalized Mathematics, 16(3): 247–252, 2008. doi:10.2478/v10037-008-0029-8.Open DOISearch in Google Scholar

[15]Antoni Smoluk. Statystyka w XXI wieku. Przyszłość statystyki. Didactics of Mathematics, 14(18):59–70, 2017. doi:10.15611/dm.2017.14.06.Open DOISearch in Google Scholar