Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We discuss algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. For a certain set of 12 such sums, we show that any two numbers are algebraically independent, and that any three are algebraically independent except for those in 22 exceptional triplets. We explicitly present algebraic relations for some of these exceptional cases.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
Pages17-31
Number of pages15
Volume1385
DOIs
Publication statusPublished - 2011
EventDiophantine Analysis and Related Fields 2011, DARF - 2011 - Musashino, Tokyo, Japan
Duration: 2011 Mar 32011 Mar 5

Other

OtherDiophantine Analysis and Related Fields 2011, DARF - 2011
CountryJapan
CityMusashino, Tokyo
Period11/3/311/3/5

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Fibonacci numbers

Keywords

  • Fibonacci numbers
  • Lucas numbers
  • reciprocal sums

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Elsner, C., Shimomura, S., & Shiokawa, I. (2011). Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. In AIP Conference Proceedings (Vol. 1385, pp. 17-31) https://doi.org/10.1063/1.3630036

Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. / Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata.

AIP Conference Proceedings. Vol. 1385 2011. p. 17-31.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Elsner, C, Shimomura, S & Shiokawa, I 2011, Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. in AIP Conference Proceedings. vol. 1385, pp. 17-31, Diophantine Analysis and Related Fields 2011, DARF - 2011, Musashino, Tokyo, Japan, 11/3/3. https://doi.org/10.1063/1.3630036
Elsner C, Shimomura S, Shiokawa I. Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. In AIP Conference Proceedings. Vol. 1385. 2011. p. 17-31 https://doi.org/10.1063/1.3630036
Elsner, Carsten ; Shimomura, Shun ; Shiokawa, Iekata. / Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers. AIP Conference Proceedings. Vol. 1385 2011. pp. 17-31
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