Fibonacci Numbers (Repost)

In elementary mathematics, there are many difficult and interesting problems not connected with the name of an individual, but rather possessing the character of "mathematical folklore". Such problems are scattered throughout the wide literature of popular (or, simply, entertaining!) mathematics, and often it is very difficult to establish the source of a particular problem.
These problems often circulate in several versions. Sometimes several such problems combine into a single more complex one; sometimes the opposite happens and one problem splits up into several simple ones. Thus it is often difficult to distinguish between the end of one problem and the beginning of another. We should consider that
in each of these problems we are dealing with little mathematical theories, each with its own history, its own complex of problems and its own characteristic methods, all, however, closely connected with the history and methods of "great mathematics".
The theory of Fibonacci numbers is just such a theory. Derived from the famous "rabbit problem", going back nearly 750 years, Fibonacci numbers, even now, provide one of the most fascinating chapters of elementary mathematics. Problems connected with Fibonacci numbers occur in many popular books on mathematics, are discussed at
meetings of school mathematical societies, and feature in mathematical competitions.
The present book contains a set of problems which were the themes of several meetings of the schoolchildren*s mathematical club of Leningrad State University in the academic year 1949-50. In accordance with the wishes of those taking part, the questions discussed at these meetings were mostly number-theoretical, a theme which is
developed in greater detail here.