Pacific Journal of Mathematics

The mappings of the positive integers into themselves which preserve division

Morgan Ward

Article information

Source
Pacific J. Math., Volume 5, Suppl. 2 (1955), 1013-1023.

Dates
First available in Project Euclid: 20 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1172000966

Mathematical Reviews number (MathSciNet)
MR0075968

Zentralblatt MATH identifier
0068.03803

Subjects
Primary: 10.0X

Citation

Ward, Morgan. The mappings of the positive integers into themselves which preserve division. Pacific J. Math. 5 (1955), no. 2, 1013--1023. https://projecteuclid.org/euclid.pjm/1172000966


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References

  • [1] R.D. Carmichael, On the numerical factors of the arithmetic forms, Ann. Math. (2), 15 (1913-14), 30-70.
  • [2] R. Dedekind, Werke, Vol. 1, Brunswick (1930).
  • [3] L.E. Dickson, History, Vol. 1, Washington (1919).
  • [4] M. Hall, Divisibility sequences of the third order, mer. J. Math., 58(1936), 577-84.
  • [5] D.H. Lehmsr, Thesis:On an extended theory of Lucas functions,Ann. Math. (2), 31 (1930), 419-48.
  • [6] E. Lucas, Theorie des fonciions numeriques simplement periodiqucs, Amer. J. Math., 1 (1878), 184-240; 289-321.
  • [7] J.J. Sylvester, On certain ternary cubic form equations, Amer. J. Math., 2 (1879), 357-83.
  • [8] Morgan Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc, 45 (1939), 335-50.
  • [9] Morgan Ward, Arithmetical properties of sequences in riiigs, Ann. Math. (2), 39 (1938), 210-19.
  • [10] Morgan Ward, Arithmetical properties of polynomials associated with the Iemniscate elliptic functions, Proc. Nat. Acad. Sci., 36 (1950), 359-62.
  • [11] Morgan Ward, Residuated distributive lattices, Duke Math. J., 6 (1940), 641-51.
  • [12] Morgan Ward, Linear divisibility sequences, Trans. Amer. Math. Soc, 41 (1937), 276-86.
  • [13] Morgan Ward, The law of repetition of primes in an elliptic divisibility sequence, Duke Math. J., 15 (1948), 941-46.
  • [14] Morgan Ward, Note on divisibility sequences, Bull, Amer. Math. Soc, 42 (1936), 843-45. CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA