참고문헌
-
Lj. Bacic and A. Filipin, The extendibility of D(4)-pairs {
$F_{2k}$ ,$F_{2k+6}$ } and {$P_{2k}$ ,$P_{2k+4}$ }, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 20 (2016), 27-35. - J. H. E. Cohn, Square Fibonacci numbers, etc, Fibonacci Quart. 2 (1964), 109-113.
- J. E. Cremona, Algorithms for Modular Elliptic Curves, second edition, Cambridge University Press, Cambridge, 1997.
- L. E. Dickson, History of the Theory of Numbers. Vol. II, Chelsea Publishing Co., New York, 1966.
- A. Dujella, A proof of the Hoggatt-Bergum conjecture, Proc. Amer. Math. Soc. 127 (1999), no. 7, 1999-2005. https://doi.org/10.1090/S0002-9939-99-04875-3
- A. Dujella, A parametric family of elliptic curves, Acta Arith. 94 (2000), no. 1, 87-101. https://doi.org/10.4064/aa-94-1-87-101
- A. Dujella, Diophantine m-tuples and elliptic curves, J. Theor. Nombres Bordeaux 13 (2001), no. 1, 111-124. https://doi.org/10.5802/jtnb.308
- A. Dujella, Diophantine quadruples and Fibonacci numbers, Bull. Kerala Math. Assoc. 1 (2004), no. 2, 133-147.
- A. Dujella and A. Petho, Integer points on a family of elliptic curves, Publ. Math. Debrecen 56 (2000), no. 3-4, 321-335.
-
A. Filipin, The extendibility of D(4)-pair {
$F_{2k}$ ,$5F_{2k}$ }, Fibonacci Quart. 53 (2015), no. 2, 124-129. - A. Filipin, Y. Fujita, and A. Togbe, The extendibility of Diophantine pairs I: the general case, Glas. Mat. Ser. III 49(69) (2014), no. 1, 25-36. https://doi.org/10.3336/gm.49.1.03
- A. Filipin, Y. Fujita, and A. Togbe, The extendibility of Diophantine pairs II: Examples, J. Number Theory 145 (2014), 604-631. https://doi.org/10.1016/j.jnt.2014.06.020
-
Y. Fujita, The Hoggatt-Bergum conjecture on D(-1)-triples {
$F_{2k+1}$ ,$F_{2k+3}$ ,$F_{2k+5}$ } and integer points on the attached elliptic curves, Rocky Mountain J. Math. 39 (2009), no. 6, 1907-1932. https://doi.org/10.1216/RMJ-2009-39-6-1907 - Y. Fujita and F. Luca, On Diophantine quadruples of Fibonacci numbers, Glas. Mat. Ser. III 52(72) (2017), no. 2, 221-234. https://doi.org/10.3336/gm.52.2.02
- B. He, F. Luca, and A. Togbe, Diophantine triples of Fibonacci numbers, Acta Arith. 175 (2016), no. 1, 57-70.
- B. He, A. Togbe, and V. Ziegler, There is no Diophantine quintuple, Trans. Amer. Math. Soc. 371 (2019), no. 9, 6665-6709. https://doi.org/10.1090/tran/7573
- V. E. Hoggatt, Jr., and G. E. Bergum, A problem of Fermat and the Fibonacci sequence, Fibonacci Quart. 15 (1977), no. 4, 323-330.
- D. Husemoller, Elliptic Curves, Graduate Texts in Mathematics, 111, Springer-Verlag, New York, 1987.
- A. W. Knapp, Elliptic Curves, Mathematical Notes, 40, Princeton University Press, Princeton, NJ, 1992.
- J. B. Lee and J. Park, Some conditions on the form of third element from Diophantine pairs and its application, J. Korean Math. Soc. 55 (2018), no. 2, 425-445. https://doi.org/10.4134/JKMS.j170289
- J. Morgado, Generalization of a result of Hoggatt and Bergum on Fibonacci numbers, Portugal. Math. 42 (1983/84), no. 4, 441-445 (1986).
- K. Ono, Euler's concordant forms, Acta Arith. 78 (1996), no. 2, 101-123. https://doi.org/10.4064/aa-78-2-101-123
- SIMATH manual, Saarbrucken, 199, ATH manual, Saarbrucken, 1997.