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@book{math_body,
author = {森田 真生},
yomi = {Masao Morita},
editor = {},
title = {数学する身体},
publisher = {新潮社},
year = {2018},
note = {{ISBN:} 978-4-10-121366-8}
}
@book{fibonacci_number,
author = {中村 滋},
yomi = {Shigeru Nakamura},
editor = {},
title = {フィボナッチ数の小宇宙},
publisher = {日本評論社},
year = {2002},
note = {{ISBN:} 4-535-78281-4}
}
@book{iwanami_number_theory_2,
author = {河田 敬義},
yomi = {Yukiyoshi Kawada},
editor = {},
title = {数論 II},
publisher = {岩波書店},
year = {1978}
}
@article{DBLP:journals/siamcomp/SolovayS77,
author = {Robert Solovay and
Volker Strassen},
title = {A Fast Monte-Carlo Test for Primality},
journal = {{SIAM} J. Comput.},
volume = {6},
number = {1},
pages = {84--85},
year = {1977}
}
@article{Dickman1930,
author={Dickman, K.},
title={On the frequency of numbers containing prime factors of a certain relative magnitude},
journal={Arkiv f{\"o}r Matematik, Astronomi och Fysik},
volume={22A},
issue={10},
year={1930},
pages={1--14}
}
@inbook{Konyagin2013,
address = {New York, NY},
author = {Graham, Ronald L. and Ne{\v{s}}et{\v{r}}il, Jaroslav and Butler, Steve},
booktitle = {The Mathematics of Paul Erd{\H{o}}s I},
description = {On Primes Recognizable in Deterministic Polynomial Time | SpringerLink},
doi = {10.1007/978-1-4614-7258-2_12},
editor = {Graham, Ronald L. and Nesetril, Jaroslav and Butler, Steve},
isbn = {978-1-4614-7258-2},
pages = {159--186},
publisher = {Springer New York},
title = {On Primes Recognizable in Deterministic Polynomial Time},
type = {Publication},
url = {https://doi.org/10.1007/978-1-4614-7258-2_12},
year = 2013
}
@article{pollard_1974,
title={Theorems on factorization and primality testing},
volume={76},
DOI={10.1017/S0305004100049252},
number={3},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
publisher={Cambridge University Press}, author={Pollard, J. M.},
year={1974},
pages={521–528}
}
@inproceedings{10.1145/800116.803773,
author = {Miller, Gary L.},
title = {Riemann's Hypothesis and Tests for Primality},
year = {1975},
isbn = {9781450374194},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
doi = {10.1145/800116.803773},
booktitle = {Proceedings of the Seventh Annual ACM Symposium on Theory of Computing},
pages = {234–239},
numpages = {6},
location = {Albuquerque, New Mexico, USA},
series = {STOC '75}
}
@InProceedings{10.1007/3-540-58691-1_36,
author = {Alford, W. R.
and Granville, Andrew
and Pomerance, Carl},
editor={Adleman, Leonard M.
and Huang, Ming-Deh},
title = {On the difficulty of finding reliable witnesses},
booktitle = {Algorithmic Number Theory},
year = {1994},
publisher = {Springer Berlin Heidelberg},
address = {Berlin, Heidelberg},
pages = {1--16},
isbn = {978-3-540-49044-9},
doi = {10.1007/3-540-58691-1_36}
}
@ARTICLE{Agrawal02primesis,
author = {Manindra Agrawal and Neeraj Kayal and Nitin Saxena},
title = {PRIMES is in P},
journal = {Annals of Mathematics},
year = {2002},
volume = {2},
pages = {781--793}
}
@ARTICLE{Alford1994,
author = {W. R. Alford and Andrew Granville and Carl Pomerance},
title = {There are Infinitely Many Carmichael Numbers},
journal = {Annals of Mathematics},
year = {1994},
volume = {140},
issue = {3},
doi = {10.2307/2118576},
pages = {703–722}
}
@article{pollard:1978,
author = {Pollard, J.},
journal = {Mathematics of Computation},
keywords = {file-import-09-02-11},
pages = {918--924},
priority = {0},
title = {{Monte Carlo} methods for Index Computation (mod p)},
volume = {32},
year = {1978}
}
@article{Floyd:1967:NA:321420.321422,
author = {Floyd, Robert W.},
title = {Nondeterministic Algorithms},
journal = {J. ACM},
issue_date = {Oct. 1967},
volume = {14},
number = {4},
month = oct,
year = {1967},
issn = {0004-5411},
pages = {636--644},
numpages = {9},
url = {http://doi.acm.org/10.1145/321420.321422},
doi = {10.1145/321420.321422},
acmid = {321422},
publisher = {ACM},
address = {New York, NY, USA},
}
@article{Williams1982,
author = {H. C. Williams},
journal = {Mathematics of Computation},
pages = {225–234},
title = {A p+1 method of factoring},
volume = {39},
issue = {159},
doi = {10.2307/2007633},
year = {1982}
}
@article{Cassels1966DiophantineEW,
title={Diophantine Equations with Special Reference To Elliptic Curves},
author={John W. Cassels},
journal={Journal of The London Mathematical Society-second Series},
year={1966},
pages={193-291},
doi={10.1112/JLMS/S1-41.1.193}
}
@article{Catalan's_conjecture,
author = {Preda Mihăilescu},
doi = {doi:10.1515/crll.2004.048},
url = {https://doi.org/10.1515/crll.2004.048},
title = {Primary cyclotomic units and a proof of Catalans conjecture},
journal = {Journal für die reine und angewandte Mathematik},
number = {572},
volume = {2004},
year = {2004},
pages = {167--195}
}
@article{atkin_sieve,
title = "Prime sieves using binary quadratic forms",
author = "A.O.L. Atkin and D.J. Bernstein",
year = "2004",
doi = "10.1090/S0025-5718-03-01501-1",
volume = "73",
pages = "1023--1030",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
}
@book{A_Computational_Perspective,
author = {R. Crandall and C. Pomerance},
editor = {},
title = {素数全書 計算からのアプローチ},
publisher = {朝倉書店},
year = {2010},
note = {{ISBN:} 978-4-254-11128-6, 和田秀男監訳}
}
@article{selfridge_method,
title = "Lucas pseudoprimes",
author = "Robert Baillie and Samuel S. Wagstaff",
year = "1980",
doi = "10.1090/S0025-5718-1980-0583518-6",
volume = "35",
issue = "152",
pages = "1391--1417",
journal = "Mathematics of Computation",
}
@article{fibonacci_pseudoprimes_infinite,
title = "On the infinitude of Fibonacci pseudoprimes",
author = "E. Lehmer",
year = "1964",
volume = "2",
pages = "229--230",
journal = "Fibonacci Quarterly",
}
@article{lucas_pseudoprimes_infinite,
title = "A lower bound for the counting function of Lucas pseudoprimes",
author = "P. Erdős, P. Kiss and A. Sárközy",
year = "1988",
volume = "51",
pages = "315--323",
journal = "Math. Comp.",
doi = "10.1090/S0025-5718-1988-0942158-4",
}
@article{frobenius_pseudoprimes_infinite,
title = "Frobenius pseudoprimes",
author = "Grantham, Jon",
year = "2001",
volume = "70",
pages = "873--891",
journal = "Math. Comp.",
doi = "10.1090/S0025-5718-00-01197-2",
}
@article{divisors_lenstra,
title = "Divisors in Residue Classes",
author = "H. W. Lenstra, Jr.",
year = "1984",
volume = "42",
pages = "331--340",
journal = "Math. Comp.",
doi = "10.2307/2007582",
}
@article{RichardJ1995,
author = {Richard J. McIntosh},
journal = {Acta Arithmetica},
number = {4},
pages = {381-389},
title = {On the converse of Wolstenholme's Theorem},
volume = {71},
year = {1995},
}
@article{McIntosh2007ASF,
title={A search for Fibonacci-Wieferich and Wolstenholme primes},
author={Richard J. McIntosh and Eric L. Roettger},
journal={Math. Comput.},
year={2007},
volume={76},
pages={2087-2094}
}
@article{Zhi1992,
author = {Zhi-Wei Sun},
journal = {Acta Arithmetica},
number = {4},
pages = {371-388},
title = {Fibonacci numbers and Fermat's last theorem},
volume = {60},
year = {1992},
}
@article{Booker2022,
author = {Andrew R. Booker and Shehzad Hathi and Michael J. Mossinghoff and Timothy S. Trudgian},
journal = {The Ramanujan Journal},
pages = {913-941},
title = {Wolstenholme and Vandiver primes},
volume = {58},
year = {2022},
doi = {10.1007/s11139-021-00438-3}
}
@article{Lukes1996,
author = {R. F. Lukes and C. D. Patterson and H. C. Williams},
journal = {Mathematics of Computation},
pages = {361-372},
title = {Some Results on Pseudosquares},
volume = {65},
year = {1996},
}
@InProceedings{10.1007/978-3-642-14518-6_26,
author="Sorenson, Jonathan P.",
editor="Hanrot, Guillaume
and Morain, Fran{\c{c}}ois
and Thom{\'e}, Emmanuel",
title="Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures",
booktitle="Algorithmic Number Theory",
year="2010",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="331--339",
isbn="978-3-642-14518-6"
}
@article{Strassen1976/77,
author = {Strassen, Volker},
journal = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
language = {ger},
pages = {1-8},
title = {Einige Resultate über Berechnungskomplexität.},
url = {http://eudml.org/doc/146659},
volume = {78},
year = {1976/77},
}
@article{10.1112/blms/28.4.351,
author = {Mckee, James},
title = "{Turning Euler's Factoring Method into a Factoring Algorithm}",
journal = {Bulletin of the London Mathematical Society},
volume = {28},
number = {4},
pages = {351-355},
year = {1996},
month = {06},
issn = {0024-6093},
doi = {10.1112/blms/28.4.351},
url = {https://doi.org/10.1112/blms/28.4.351},
eprint = {https://academic.oup.com/blms/article-pdf/28/4/351/1232572/28-4-351.pdf},
}
@article{10.1007/BF01457454,
author = {A. K. Lenstra and H. W. Lenstra Jr. and L. Lovász},
title = {Factoring polynomials with rational coefficients},
journal = {Mathematische Annalen},
volume = {261},
year = {1982},
issue = {4},
pages = {515--534},
doi = {10.1007/BF01457454}
}
@InProceedings{10.1007/3-540-68339-9_14,
author="Coppersmith, Don",
editor="Maurer, Ueli",
title="Finding a Small Root of a Univariate Modular Equation",
booktitle="Advances in Cryptology --- EUROCRYPT '96",
year="1996",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="155--165",
isbn="978-3-540-68339-1"
}
@InProceedings{10.1007/3-540-68339-9_16,
author="Coppersmith, Don",
editor="Maurer, Ueli",
title="Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known",
booktitle="Advances in Cryptology --- EUROCRYPT '96",
year="1996",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="178--189",
isbn="978-3-540-68339-1"
}
@article{10.1007/s001459900030,
author = {Coppersmith, Don},
title = {Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities},
journal = {Journal of Cryptology},
volume = {10},
year = {1997},
pages = {233--260},
doi = {10.1007/s001459900030}
}
@InProceedings{10.1007/BFb0024458,
author="Howgrave-Graham, Nicholas",
editor="Darnell, Michael",
title="Finding small roots of univariate modular equations revisited",
booktitle="Crytography and Coding",
year="1997",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="131--142",
isbn="978-3-540-69668-1"
}
@misc{wiki:Shanks's_square_forms_factorization,
author = "Wikipedia",
title = "{Shanks's square forms factorization} --- {W}ikipedia{,} The Free Encyclopedia",
year = "2022",
howpublished = {\url{http://en.wikipedia.org/w/index.php?title=Shanks's\%20square\%20forms\%20factorization&oldid=1094553504}},
note = "[Online; accessed 23-November-2022]"
}
@article{Lehman1974FactoringLI,
title={Factoring large integers},
author={R. Sherman Lehman},
journal={Mathematics of Computation},
year={1974},
volume={28},
pages={637-646}
}
@article{Saidak2006,
title={A New Proof of Euclid's Theorem},
author={Filip Saidak},
journal={The American Mathematical Monthly},
year={2006},
volume={113},
number={10},
doi={10.2307/27642094},
pages={937-938}
}
@article{Sierpinski1960,
title={Sur un problème concernant les nombres $k \cdot 2^n + 1$},
author={Wacław Sierpiński},
journal={Elem. Math.},
year={1960},
pages={73-74}
}
@article{PeraltaOkamoto1996,
title={Faster factoring of integers of a special form},
author={René Peralta and Eiji Okamoto},
journal={IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Sciences},
year={1996},
volume={E79-A},
number={4},
pages={489-493}
}
@InProceedings{10.1007/978-3-0348-8295-8_11,
author="Peralta, Ren{\'e}",
title="Elliptic Curve Factorization Using a ``Partially Oblivious'' Function",
booktitle="Cryptography and Computational Number Theory",
year="2001",
publisher="Birkh{\"a}user Basel",
pages="123--128",
isbn="978-3-0348-8295-8"
}