4 papers
Sums of Reciprocals of Recurrence Relations
Hao Cui, Xiaoyu Cui, Sophia C. Davis +7
There is a growing literature on sums of reciprocals of polynomial functions of recurrence relations with constant coefficients and fixed depth, such as Fibonacci and Tribonacci nu…
Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples
Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller +1
Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves; for the first, we have a parametrization through rational points on the unit circle, an…
Benford Behavior of Generalized Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by and , every…
Benford Behavior of Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers . A set $S \subset \…