On sums of pairs of squares and cubes

J. V. Leyendekkers, J. H. Clarke and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 4, 1998, Number 3, Pages 108—112
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Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006, Australia

J. H. Clarke
University of Technology,
Sydney (UTS), 2007, Australia

A. G. Shannon
University of Technology, Sydney, 2007, Australia

AMS Classification

  • 11D09
  • 11D 25
  • 11B3S

References

  1. Burton, David M 1980 Elementary Number Theory Boston: AlSyn and Bacon
  2. Dickson, L.E. 1952. History of the Theory’ of Numbers, Volume 2. New York. Chelsea.
  3. Ewell, J.A 1983 A simple proof of Fermat’s two-square theorem. American Mathematical Monthly. 90: 635-637.
  4. Hoggatt, Verner E. Jr. 1969 Fibonacci and Lucas Numbers Boston. Houghton Mifflin.
  5. Horadam, A.F. 1961. Fibonacci number triples American Mathematical Monthly, 68,8: 751-753
  6. Hunter, J, 1964. Number Theory. Edinburgh: Oliver and Boyd
  7. Leyendekkers, J.V., Rybak, J.M. and Shannon, A.G 1997. The anatomy of odd- exponent Diophantine triples. Notes on Number Theory & Discrete Mathematics. 3.1: 34-44.
  8. MacMahon, Percy A. 1915. Combinatory Analysis Volume 1. Cambridge Cambridge University Press
  9. Melham, R.S. (Submitted). Some analogues of the identity
  10. Melharn, R.S. (Submitted). Families of identities involving sums of powers of the Fibonacci and Lucas numbers.
  11. van der Poorten, Alf. 1996. Notes on Fermat’s Last Theorem. New York: Wiley- Interscience.
  12. Shannon, A.G. and Horadarn, A F. 1973. Generalized Fibonacci number triples. American Mathematical Monthly, 80.2; 187-190.
  13. Shannon, A.G. and Horadam, A.F. 1979. Special recurrence relations associated with the sequence {wn(a,b:p,q)}. The Fibonacci Quarterly. 1 7A: 294-299.
  14. Vorob’ev, N.N. 1961 Fibonacci Numbers. New York: Pergamon.

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Cite this paper

Leyendekkers, J. V., Clarke, J. H. & Shannon, A. G. (1998). On sums of pairs of squares and cubes. Notes on Number Theory and Discrete Mathematics, 4(3), 108-112.

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