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On Square-Free Numbers Cover

On Square-Free Numbers

Formalized Mathematics
Volume 21 (2013): Issue 2 (June 2013)
By: Adam Grabowski  
Open Access
|Jun 2013

References

  1. [1] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.10.1007/978-3-662-05412-3
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. K¨onig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
    Search in Google Scholar
  4. [4] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  5. [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  6. [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  7. [7] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
    Search in Google Scholar
  9. [9] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
    Search in Google Scholar
  10. [10] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
    Search in Google Scholar
  11. [11] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  12. [12] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  13. [13] Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
    Search in Google Scholar
  14. [14] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  15. [15] Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Formalized Mathematics, 2(4):453-459, 1991.
    Search in Google Scholar
  16. [16] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
    Search in Google Scholar
  17. [17] Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin’s test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.
    Search in Google Scholar
  18. [18] G.H. Hardy and E.M. Wright. An Introduction to the Theory of Numbers. Oxford University Press, 1980.
    Search in Google Scholar
  19. [19] Magdalena Jastrz¸ebska and Adam Grabowski. On the properties of the M¨obius function. Formalized Mathematics, 14(1):29-36, 2006. doi:10.2478/v10037-006-0005-0.10.2478/v10037-006-0005-0
    Search in Google Scholar
  20. [20] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
    Search in Google Scholar
  21. [21] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4): 573-577, 1997.
    Search in Google Scholar
  22. [22] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181-187, 2005.
    Search in Google Scholar
  23. [23] Artur Korniłowicz and Piotr Rudnicki. Fundamental Theorem of Arithmetic. Formalized Mathematics, 12(2):179-186, 2004.
    Search in Google Scholar
  24. [24] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  25. [25] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
    Search in Google Scholar
  26. [26] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
    Search in Google Scholar
  27. [27] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
    Search in Google Scholar
  28. [28] Xiquan Liang, Li Yan, and Junjie Zhao. Linear congruence relation and complete residue systems. Formalized Mathematics, 15(4):181-187, 2007. doi:10.2478/v10037-007-0022-7.10.2478/v10037-007-0022-7
    Search in Google Scholar
  29. [29] Robert Milewski. Natural numbers. Formalized Mathematics, 7(1):19-22, 1998.
    Search in Google Scholar
  30. [30] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Formalized Mathematics, 6(2):265-268, 1997.
    Search in Google Scholar
  31. [31] Hiroyuki Okazaki and Yasunari Shidama. Uniqueness of factoring an integer and multiplicative group Z/pZ*. Formalized Mathematics, 16(2):103-107, 2008. doi:10.2478/v10037-008-0015-1.10.2478/v10037-008-0015-1
    Search in Google Scholar
  32. [32] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
    Search in Google Scholar
  33. [33] Konrad Raczkowski and Andrzej Nedzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.
    Search in Google Scholar
  34. [34] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
    Search in Google Scholar
  35. [35] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
    Search in Google Scholar
  36. [36] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
    Search in Google Scholar
  37. [37] Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.
    Search in Google Scholar
  38. [38] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
    Search in Google Scholar
  39. [39] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
    Search in Google Scholar
  40. [40] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  41. [41] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
    Search in Google Scholar
  42. [42] Stanisław Zukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215-222, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/forma-2013-0017 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 153 - 162
Published on: Jun 1, 2013
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
square-free numbers,
prime reciprocals,
lattice of natural divisors
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2013 Adam Grabowski, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 21 (2013): Issue 2 (June 2013)