1, 1, 2, 3, 5, 8, 13, 21, 34. . . Look carefully. Do you see the pattern? Each number above is the sum of the two numbers before it. Though most of us are unfamiliar with it, this numerical series, called the Fibonacci sequence, is part of a code that can be found everywhere in nature. Count the petals on a flower or the peas in a peapod. The ...
Since at least the time of Poisson, mathematicians have pondered the notion of recurrence for differential equations. Solutions that exhibit recurrent behavior provide insight into the behavior of general solutions. In Recurrence and Topology, Alongi and Nelson provide a modern understanding of the subject, using the language and tools of ...
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact ...
A result due to Hasse says that, on average, 17 out of 24 consecutive primes will divide a number in the sequence $U_n = 2^n+1$. There are few sequences of integers for which this relative density can be computed exactly. In this work, Ballot links Hasse's method to the concept of the group associated with the set of second-order recurring ...
Primer booklet which explains and describes the fascinating Fibonacci number sequence, and how it is utilized by traders to forecast and interpret price action. Comprehensive bibliography lists all known references on this subject.
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