@article{BHV,
 author={Bilu, Yuri and Hanrot, Guillaume and Voutier, Paul M.},
 title={Existence of primitive divisors of {Lucas} and {Lehmer} numbers},
 journal={Journal f\"ur die reine und angewandte Mathematik},
 volume={539}, pages={75--122}, year={2001},
 doi={10.1515/crll.2001.080},
 note={With an appendix by M. Mignotte. Definitions in Section 1, Theorem A (Carmichael--Ward), and Theorem 1.4},
 url={https://doi.org/10.1515/crll.2001.080}
}
@article{Bernstein,
 author={Bernstein, Daniel J.}, title={Factoring into coprimes in essentially linear time},
 journal={Journal of Algorithms}, volume={54}, number={1}, pages={1--30}, year={2005},
 note={Context for coprime refinement; no complexity bound from this article is used},
 url={https://cr.yp.to/coprimes.html}
}
@misc{ConradPell,
 author={Conrad, Keith}, title={Pell's equation, {I}},
 howpublished={Expository notes}, year={n.d.},
 note={Theorem 2.3 (Lagrange), and Sections 4--7. Accessed 27 September 2026},
 url={https://kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn1.pdf}
}
@misc{Sutherland,
 author={Sutherland, Andrew V.}, title={The analytic class number formula},
 howpublished={MIT 18.785 Number Theory I, Lecture 19}, year={2017},
 note={Theorems 19.12 and 19.15, Fall 2017 lecture notes},
 url={https://math.mit.edu/classes/18.785/2017fa/LectureNotes19.pdf}
}
@misc{DLMF,
 author={{NIST}}, year={n.d.}, title={Digital Library of Mathematical Functions},
 howpublished={Sections 27.9, 27.11 and 27.12},
 note={Quadratic characters and fixed-modulus prime estimates, in particular Eq. 27.12.8. Accessed 28 September 2026},
 url={https://dlmf.nist.gov/27}
}
@misc{BardestaniFreiberg,
 author={Bardestani, Mohammad and Freiberg, Tristan},
 title={Mertens's theorem for splitting primes and more---a concise and adaptable proof of {Hardy}},
 year={2013}, howpublished={arXiv:1309.7482v1},
 note={Theorem 3.3 and the following fixed-modulus error estimate},
 url={https://arxiv.org/abs/1309.7482v1}
}
@article{Teravainen,
 author={Ter{\"a}v{\"a}inen, Joni},
 title={On the {Liouville} function at polynomial arguments},
 journal={American Journal of Mathematics}, volume={146}, number={4}, pages={1115--1167}, year={2024}, doi={10.1353/ajm.2024.a932436},
 note={Locators refer to arXiv:2010.07924v4: Definition 2.8, Theorem 2.9, Proposition 2.10 and Section 6},
 url={https://arxiv.org/abs/2010.07924v4}
}
@article{Gorodetsky,
 author={Gorodetsky, Ofir}, title={A {Kubilius} model for sieve-theoretic sequences},
 journal={Analysis Mathematica}, year={2026}, doi={10.1007/s10476-026-00178-w},
 note={Published online 14 August 2026. The valuation-comparison locator is Theorem 2.3 of arXiv:2608.14190v1},
 url={https://arxiv.org/abs/2608.14190v1}
}
@article{MSW,
 author={M{\'e}rai, L{\'a}szl{\'o} and Shparlinski, Igor E. and Winterhof, Arne},
 title={Character sums over sparse elements of finite fields},
 year={2024}, journal={Bulletin of the London Mathematical Society}, volume={56}, number={4}, pages={1488--1510}, doi={10.1112/blms.13008},
 note={The locator is Lemma 3.1 of arXiv:2211.08452v1, used only as a stated form of the classical mixed Weil bound},
 url={https://arxiv.org/abs/2211.08452v1}
}

@article{ESTW,
 author={Everest, Graham and Stevens, Shaun and Tamsett, Duncan and Ward, Tom},
 title={Primes generated by recurrence sequences},
 journal={The American Mathematical Monthly}, volume={114}, number={5},
 pages={417--431}, year={2007}, doi={10.1080/00029890.2007.11920430},
 note={Locators refer to arXiv:math/0412079v2: Lemma 4.1, Proposition 4.2 and Theorem 5.1},
 url={https://arxiv.org/abs/math/0412079v2}
}
@article{BCG,
 author={Borwein, Peter and Choi, Stephen K. K. and Ganguli, Himadri},
 title={Sign changes of the {Liouville} function on quadratics},
 journal={Canadian Mathematical Bulletin}, volume={56}, number={2},
 pages={251--257}, year={2013}, doi={10.4153/CMB-2011-166-9},
 note={Theorem 2.2 of arXiv:1109.3107v1},
 url={https://arxiv.org/abs/1109.3107v1}
}
@article{Srinivasan,
 author={Srinivasan, Anitha},
 title={Infinitely many sign changes of the {Liouville} function on {$x^2+d$}},
 journal={Proceedings of the American Mathematical Society}, volume={150}, number={9},
 pages={3799--3809}, year={2022}, doi={10.1090/proc/15939},
 note={Theorem 1.3 of arXiv:2104.15004v2},
 url={https://arxiv.org/abs/2104.15004v2}
}
@misc{dBWX,
 author={de la Bret{\`e}che, R{\'e}gis and Wang, Victor Y. and Xu, Max Wenqiang},
 title={Random multiplicative functions and making squares from polynomial values},
 year={2026}, howpublished={arXiv:2607.06398v1},
 note={Introduction and Sections 5--7; contextual comparison, not a proof input},
 url={https://arxiv.org/abs/2607.06398v1}
}
@misc{Mine,
 author={Mine, Masahiro},
 title={An upper bound for the number of smooth values of a polynomial and its applications},
 year={2025}, howpublished={arXiv:2410.09558v2},
 note={Revised 8 October 2025. Section 1.3, Theorem 1.4 and Corollary 1.5; contextual comparison},
 url={https://arxiv.org/abs/2410.09558v2}
}
@article{Hamming,
 author={Hamming, Richard W.},
 title={Error detecting and error correcting codes},
 journal={Bell System Technical Journal}, volume={29}, number={2},
 pages={147--160}, year={1950}, doi={10.1002/j.1538-7305.1950.tb00463.x}
}
@article{Hoeffding,
 author={Hoeffding, Wassily},
 title={Probability inequalities for sums of bounded random variables},
 journal={Journal of the American Statistical Association}, volume={58}, number={301},
 pages={13--30}, year={1963}, doi={10.1080/01621459.1963.10500830}
}