Autors: Dimitrov, S. I.
Title: Pairs of square-free values of the type n^2+1, n^2+2
Keywords: square-free number; asymptotic formula; Kloosterman sum

Abstract: We show that there exist infinitely many consecutive square-free numbers of the form n^2+1, n^2+2. We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive number.

References

    Issue

    Czechoslovak Math. J., vol. 71, issue 4, pp. 991 -- 1009, 2021, Czech Republic, Springer, https://doi.org/10.21136/CMJ.2021.0165-20

    Цитирания (Citation/s):
    1. B. Chen, On the consecutive square-free values of the polynomials x_1^2+...+x_k^2+1, x_1^2+...x_k^2+2, Indian J. Pure Appl. Math., (ISSN : 0019-5588 (print), 0975-7465 (online)), vol 54, 3, (2023), 743 -- 756, (https://doi.org/10.1007/s13226-022-00292-z). - 2023 - в издания, индексирани в Scopus и/или Web of Science
    2. Y. Feng, Consecutive square-free values of the type x^2+y^2+z^2+k, x^2+y^2+z^2+k+1, Czechoslovak Math. J. (ISSN : 0011-4642 (print), ISSN : 1572-9141 (online)), vol. 73, 1, (2023), 297 -- 310, (https://doi.org/10.21136/CMJ.2022.0154-22). - 2023 - в издания, индексирани в Scopus и/или Web of Science
    3. G. Chen, W. Wang, On the r-free values of the polynomial x^2+y^2+z^2+k, Czechoslovak Math. J., (ISSN : 0011-4642 (print), ISSN : 1572-9141 (online)), vol. 73, 3, (2023), 955 -- 969, (https://doi.org/10.21136/CMJ.2023.0394-22). - 2023 - в издания, индексирани в Scopus и/или Web of Science
    4. L. Vaishya, M. Pandey, Counting square-free integers represented by binary quadratic forms of a fixed discriminant, Arch. Math., (ISSN: 0003-889X (print), ISSN: 1420-8938 (online)), vol. 121, 4, (2023), 385 -- 395, (https://doi.org/10.1007/s00013-023-01915-5). - 2023 - в издания, индексирани в Scopus и/или Web of Science

    Вид: статия в списание, публикация в издание с импакт фактор, индексирана в Scopus