Citation: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 11, pages 223–226 (2017)
Abstract. We present a case study on a formalization of a textbook theorem that is listed as \#39 at Freek Wiedijk's list of ``Top 100 mathematical theorems''. We focus on the formalization of the theorem that Pell's equation $x^2-Dy^2 = 1$ has infinitely many solutions in positive integers for a given non square natural number $D$.We present also a formalization of the theorem that based on the least fundamental solution of the equation we can simply calculate algebraically each remaining solution.
- A. Grabowski, “Efficient rough set theory merging,” Fundamenta Informaticae, vol. 135, no. 4, pp. 371–385, October 2014. http://dx.doi.org/10.3233/FI-2014-1129
- K. Pąk, “Readable formalization of Euler’s partition theorem in Mizar,” in Intelligent Computer Mathematics – International Conference, CICM 2015, Washington, DC, USA, July 13–17, 2015, Proceedings, 2015. http://dx.doi.org/10.1007/978-3-319-20615-8_14 pp. 211–226.
- G. Bancerek, C. Bylinski, A. Grabowski, A. Korniłowicz, R. Matuszewski, A. Naumowicz, K. Pąk, and J. Urban, “Mizar: State-of-the-art and beyond,” in Intelligent Computer Mathematics - International Conference, CICM 2015, ser. LNCS, vol. 9150. Springer, 2015. doi: 10.1007/978-3-319-20615-8_17 pp. 261–279.
- W. Sierpiński, Elementary theory of numbers, A. Schinzel, Ed. Mathematical Institute of the Polisch Academy of Science, 1964.
- J. Harrison, “The HOL Light system REFERENCE,” 2014, http://www.cl.cam.ac.uk/ jrh13/hol-light/reference.pdf.
- N. D. Megill, “Metamath: A Computer Language for Pure Mathematics,” 2007, http://us.metamath.org/downloads/metamath.pdf.
- G. Bancerek, “Cardinal arithmetics,” Formalized Mathematics, vol. 1, no. 3, pp. 543–547, 1990.