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Experimental Mathematics Volume 31, 2022 - Issue 1
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Original Articles

On Consecutive 1’s in Continued Fractions Expansions of Square Roots of Prime Numbers

Piotr MiskaFaculty of Mathematics and Computer Science, Institute of Mathematics, Jagiellonian University, Kraków, PolandView further author information
&
Maciej UlasFaculty of Mathematics and Computer Science, Institute of Mathematics, Jagiellonian University, Kraków, PolandCorrespondence[email protected]
View further author information
Pages 238-251 | Published online: 01 May 2019

References

  • [Friesen 88] C. Friesen. “On continued fractions of given period.” Proc. Amer. Math. Soc. 103:1 (1988), 9–14.
  • [Iwaniec 74] H. Iwaniec. “Primes represented by quadratic polynomials in two variables.” Acta Arith. 24:5 (1974), 435–459.
  • [Iwaniec and Kowalski 04] H. Iwaniec and E. Kowalski. Analytic Number Theory, vol. 53. Colloquium Publications, American Math. Society, 2004.
  • [Khinchin 68] A. Y. Khinchin. Continued Fractions, Phoenix Books (Third edition). Chicago and London: The University of Chicago Press, 1968.
  • [Kuzmin 28] R. Kuzmin. “Ob odnoi zadache Gaussa.” Doklady Akad. Nauk, Ser. A. (1928), 375–380.
  • [Schinzel and Sierpiński 58] A. Schinzel and W. Sierpiński. “Sur certaines hypothèses concernant les nombres premiers.” Acta Arith. 4: 3 (1958), 185–208. Erratum: ibid. 5 (1959), 259.
  • [Skałba 16] M. Skałba. “On the equation a2+bc=n with restricted unknowns.” Bull. Polish Acad. Sci. Math. 64 (2016), 137–145.
  • [Swinnerton-Dyer 97] P. Swinnerton-Dyer. “Some applications of Schinzel’s Hypothesis to Diophantine equations.” Number Theory in Progress: Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997, pp. 503–530.
  • [Vinogradov 04] I. M. Vinogradov. Method of Trigonometrical Sums in the Theory of Numbers. Mineola, NY: Dover Publications, 2004.

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