Despite the large number of references, no systematic attempt has been made
to trace the history of major results that have influenced the subject. No single
book on the history of this huge topic could hope to be definitive. However
Leonardo of Pisa notwithstanding it is reasonable to view the modern study of
the arithmetic of recurrence sequences as having been given essential impetus by
the remarkable work of Frangois Edouard Anatole Lucas (1842-1891); many of the
themes developed in this book originate in his papers (see [283] and [1354] for
some background on his life and work, and [517] for a full list of his publications
and some of his unpublished work).
The bibliography reflects the interests and biases of the authors, and some of
the entries are to preliminary works. The authors extend their thanks to the many
workers whose contributions have given them so much pleasure and extend their
apologies to those whose contributions have not been cited. The authors also thank
many people for help with corrections and references, particularly Christian Ballot,
Daniel Berend, Keith Briggs, Sheena Brook, Susan Everest, Robert Laxton, Pieter
Moree, Patrick Moss, Wladyslaw Narkiewicz, James Propp, Michael Somos, Shaun
Stevens, Zhi-Wei Sun and Alan Ward.
Alf van der Poorten &: Igor Shparlinski Graham Everest & Thomas Ward
Centre for Number Theory Research School of Mathematics
Macquarie University University of East Anglia
Sydney Norwich
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