Prime Representing Polynomial

Karol Pąk

doi:10.2478/forma-2021-0020

References

[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 DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article
[5] James P. Jones. Universal diophantine equation. Journal of Symbolic Logic, 47(4):549–571, 1982.10.2307/2273588
Search in Google Scholar Back to article
[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 Back to article
[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 DOI Search in Google Scholar Back to article
[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 Back to article
[9] Karol Pąk. The Matiyasevich theorem. Preliminaries. Formalized Mathematics, 25(4): 315–322, 2017. doi:10.1515/forma-2017-0029.
Open DOI Search in Google Scholar Back to article
[10] Karol Pąk. Diophantine sets. Part II. Formalized Mathematics, 27(2):197–208, 2019. doi:10.2478/forma-2019-0019.
Open DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article
[12] Christoph Schwarzweller. Proth numbers. Formalized Mathematics, 22(2):111–118, 2014. doi:10.2478/forma-2014-0013.
Open DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article
[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 DOI Search in Google Scholar Back to article

Prime Representing Polynomial

References

Paradigm

My account