Bicknell-Johnson, M., and Spears, C.P. Lucas Quotient Lemmas.
Congressus Numerantium 201: 273-275, 2009.

In current pertaining to asymmetric cell division and recursive phyllotaxic patterning in biologic structures, data was organized in rectangular tables with a Fibonacci number of columns. Analysis of data arising from the division of one positive Fibonacci number by another gave a surprising relationship to Lucas numbers: quotients that rounded off to Lucas numbers. That the remainders are Fibonacci numbers was known but the almost-Lucas quotients in the lemmas following seem to be new.    

View Article