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Prime Representing Polynomial

   | 09 jul 2022

Cite

[1] 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

[2] 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/s10817-017-9440-6.604425130069070 Open DOISearch in Google Scholar

[3] Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, and Yasunari Shidama. Gaussian integers. Formalized Mathematics, 21(2):115–125, 2013. doi:10.2478/forma-2013-0013. Open DOISearch in Google Scholar

[4] James P. Jones. Diophantine representation of Mersenne and Fermat primes. Acta Arithmetica, 35:209–221, 1979. doi:10.4064/AA-35-3-209-221. Open DOISearch in Google Scholar

[5] James P. Jones. Universal diophantine equation. Journal of Symbolic Logic, 47(4):549–571, 1982.10.2307/2273588 Search in Google Scholar

[6] James P. Jones, Sato Daihachiro, Hideo Wada, and Douglas Wiens. Diophantine representation of the set of prime numbers. The American Mathematical Monthly, 83(6):449–464, 1976.10.1080/00029890.1976.11994142 Search in Google Scholar

[7] Yuri Matiyasevich. Primes are nonnegative values of a polynomial in 10 variables. Journal of Soviet Mathematics, 15:33–44, 1981. doi:10.1007/BF01404106. Open DOISearch in Google Scholar

[8] Yuri Matiyasevich and Julia Robinson. Reduction of an arbitrary diophantine equation to one in 13 unknowns. Acta Arithmetica, 27:521–553, 1975.10.4064/aa-27-1-521-553 Search in Google Scholar

[9] Karol Pąk. The Matiyasevich theorem. Preliminaries. Formalized Mathematics, 25(4): 315–322, 2017. doi:10.1515/forma-2017-0029. Open DOISearch in Google Scholar

[10] Karol Pąk. Diophantine sets. Part II. Formalized Mathematics, 27(2):197–208, 2019. doi:10.2478/forma-2019-0019. Open DOISearch in Google Scholar

[11] Karol Pąk. Formalization of the MRDP theorem in the Mizar system. Formalized Mathematics, 27(2):209–221, 2019. doi:10.2478/forma-2019-0020. Open DOISearch in Google Scholar

[12] Christoph Schwarzweller. Proth numbers. Formalized Mathematics, 22(2):111–118, 2014. doi:10.2478/forma-2014-0013. Open DOISearch in Google Scholar

[13] Zhi-Wei Sun. Further results on Hilbert’s Tenth Problem. Science China Mathematics, 64:281–306, 2021. doi:10.1007/s11425-020-1813-5. Open DOISearch in Google Scholar

[14] Rafał Ziobro. Prime factorization of sums and differences of two like powers. Formalized Mathematics, 24(3):187–198, 2016. doi:10.1515/forma-2016-0015. Open DOISearch in Google Scholar

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Computer Sciences, other, Mathematics, General Mathematics