Number Theory

Sequences and Sets

11Bxx

  1. S. Akhtari, A. Togbé, and P. G. Walsh, On the equation aX4-bY2 = 2, Acta Arith. 131 (2008), no. 2, 145–169.[MR]
  2. Huseyin Aydin, Ramazan Dikici, and Geoff C. Smith, Wall and Vinson revisited, Applications of Fibonacci Numbers, Vol. 5 (St. Andrews, 1992), Kluwer Acad. Publ., Dordrecht, 1993, pp. 61–68.[MR]
  3. Alexander Berkovich and William C. Jagy, Ternary quadratic forms, modular equations and certain positivity conjectures, The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, Springer, New York, 2009, pp. 211–241.[doi]
  4. A. Bremner and N. Tzanakis, Lucas sequences whose 12th or 9th term is a square, J. Number Theory 107 (2004), no. 2, 215–227.[MR]
  5. A. Bremner and N. Tzanakis, Lucas sequences whose 8th term is a square, preprint (2004), 44 pages.[arXiv]
  6. A. Bremner and N. Tzanakis, On squares in Lucas sequences, J. Number Theory 124 (2007), no. 2, 511–520.[MR]
  7. Florian Breuer, Ernest Lötter, and Brink van der Merwe, Ducci-sequences and cyclotomic polynomials, Finite Fields Appl. 13 (2007), no. 2, 293–304.[MR]
  8. N. Bruin, K. Győry, L. Hajdu, and Sz. Tengely, Arithmetic progressions consisting of unlike powers, Indag. Math. (N.S.) 17 (2006), no. 4, 539–555.[MR]
  9. Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek, On Fibonacci numbers with few prime divisors, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 2, 17–20.[MR]
  10. Yann Bugeaud, Maurice Mignotte, and Samir Siksek, Sur les nombres de Fibonacci de la forme qkyp, C. R. Math. Acad. Sci. Paris 339 (2004), no. 5, 327–330.[MR]
  11. Enrique Gonzalez-Jimenez and Xavier Xarles, Five squares in arithmetic progression over quadratic fields, preprint (2009), 24 pages.[arXiv]
  12. Everett W. Howe, Higher-order Carmichael numbers, Math. Comp. 69 (2000), no. 232, 1711–1719.[MR]
  13. Benjamin Kane, Representing sets with sums of triangular numbers, Int. Math. Res. Not. IMRN (2009), no. 17, 3264–3285.[MR]
  14. Tünde Kovács, Combinatorial numbers in binary recurrences, Period. Math. Hungar. 58 (2009), no. 1, 83–98.[MR/doi]
  15. J. McLaughlin, Small prime powers in the Fibonacci sequence, preprint (2002), 22 pages.[arXiv]
  16. A. Stoimenow, Generating functions, Fibonacci numbers and rational knots, J. Algebra 310 (2007), no. 2, 491–525.[MR]