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 The generalized Fibonacci sequence (the th term of which is denoted
) is defined recursively by the following statements:
Note that the regular Fibonacci numbers can be denoted by in this notaion.

means that has the following properties:
 .

.
 is the least positive integer satisfying these properties.

means that has the following properties:
 .

.

.
 is the least positive integer satisfying these properties.
Note: is then the function that gives the period of the generalized
Fibonacci sequence in modulo .
Gregory Stoll
20000408