JP Journal of Algebra, Number Theory and Applications
Volume 28, Issue 1, Pages 13 - 43
(February 2013)
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FURTHER RESULTS ON DERIVING FIBONACCI UNIFORM POWER IDENTITIES
George A. Hisert
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Abstract: This paper shows that every uniform power function of power p of Fibonacci and Lucas numbers can be expressed alternatively both as and as The proof also includes the proof of R. S. Melham’s conjectures on certain classes of Fibonacci identities. Formulae and algorithms for the calculation of coefficients for such identities are set forth. The analysis is then expanded to apply to recurrence sequences in the form
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Keywords and phrases: Fibonacci, Lucas, identity, uniform power, primitive identity, congruent identity, generalized recurrence sequence, Melham’s conjecture, uniform power function, uniform power sum, uniform power identity, UPI, Lucasian twin, base sequence, Lucas sequence, Hyper-Lucas sequence. |
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