The Matiyasevich Theorem. Preliminaries

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Summary

In this article, we prove selected properties of Pell’s equation that are essential to finally prove the Diophantine property of two equations. These equations are explored in the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.

[1] Marcin Acewicz and Karol Pak. Pell’s equation. Formalized Mathematics, 25(3):197-204, 2017. doi: 10.1515/forma-2017-0019.

[2] Zofia Adamowicz and Paweł Zbierski. Logic of Mathematics: A Modern Course of Classical Logic. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Wiley-Interscience, 1997.

[3] Martin Davis. Hilbert’s tenth problem is unsolvable. The American Mathematical Monthly, Mathematical Association of America, 80(3):233-269, 1973. doi: 10.2307/2318447.

[4] Yoshinori Fujisawa and Yasushi Fuwa. The Euler’s function. Formalized Mathematics, 6 (4):549-551, 1997.

[5] Xiquan Liang, Li Yan, and Junjie Zhao. Linear congruence relation and complete residue systems. Formalized Mathematics, 15(4):181-187, 2007. doi: 10.2478/v10037-007-0022-7.

[6] Robert Milewski. Natural numbers. Formalized Mathematics, 7(1):19-22, 1998.

[7] Rafał Ziobro. Fermat’s Little Theorem via divisibility of Newton’s binomial. Formalized Mathematics, 23(3):215-229, 2015. doi: 10.1515/forma-2015-0018.

Formalized Mathematics

(a computer assisted approach)

Journal Information

SCImago Journal Rank (SJR) 2017: 0.119
Source Normalized Impact per Paper (SNIP) 2017: 0.237



Target Group

researchers in the fields of formal methods and computer-checked mathematics

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