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89.57 Non-existence of Fibonacci and Lucas numbers in amicable pairs of opposite parity

Published online by Cambridge University Press:  01 August 2016

John H. Jaroma  and
James M. Mitchell
John H. Jaroma
Affiliation:
Department of Math. & Comp. Sci., Austin College, Sherman, TX 75090, USA, e-mail: jjaroma@austincollege.edu
James M. Mitchell
Affiliation:
Department of Chemistry, Austin College, Sherman, TX 75090, USA, e-mail: jmitchell@austincollege.edu
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Abstract

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Information
The Mathematical Gazette , Volume 89 , Issue 516 , November 2005 , pp. 451 - 454
Copyright
Copyright © The Mathematical Association 2005

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References

1. Pedersen, J. M., Known amicable pairs, http://amicable.homepage.dk/knwap.htm Google Scholar
2. García, M., Pedersen, J. M., and te Riele, H. J. J., Amicable pairs, a survey. In: High primes and misdemeanours: Lectures in honour of the 60th birthday of Hugh Cowie Williams, der Poorten, Alf van and Stein, Andreas (eds), Fields Institute Communications, Amer. Math. Soc. (2004) pp. 179–196,Google Scholar
3. Lee, E. J. and Madachy, J. S., The history and discovery of amicable numbers, J. Ree. Math. 5 (1972) Part 1 pp. 77–93, Part 2 pp. 153–173, Part 3 pp. 231–249. Errata in 6, (1973) p. 53, p. 164 and p. 229.Google Scholar
4. Guy, R. K., Unsolved problems in number theory (3rd ed.), Springer Verlag (2004).Google Scholar
5. Gioia, A. A. and Vaidya, A. M., Amicable numbers with opposite parity, Amer. Math. Monthly, 74 8 (1967) pp. 969–973.Google Scholar
6. Cohn, J. H. E., On square Fibonacci numbers, J. London Math. Soc. 39 (1964) pp. 537–541.Google Scholar
7. Cohn, J. H. E., Square Fibonacci numbers, etc., Fibonacci Quarterly 2, (1964) pp. 109–113.Google Scholar
8. Cohn, J. H. E., Lucas and Fibonacci numbers and some Diophantine equations, Proc. Glasgow Math. Assoc. 7 (1965) pp. 24–28.Google Scholar
9. Dickson, L. E., Theorems and tables on the sum of the divisors of a number, Quart. J. Math. 44 (1913) pp. 264–296.Google Scholar
10. McDaniel, W. L. and Ribenboim, P., The square terms in Lucas sequences, J. Number Theory 58 (1996) pp. 104–123.Google Scholar