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- The 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 Fibonacci-
sequence in modulo
.
means that
has the following properties:
is the number of
that are congruent to
, where
goes from
to
, inclusive.
-
means that
has the following properties:
is the number of
that are congruent to
, where
goes from
to
, inclusive.
(known as the Euler phi function) means that
has the following
properties:
is the number of
such that
, where
goes from
to
,
inclusive.
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Gregory Stoll
2000-04-08