- The Fibonacci sequence (the th term of which is denoted )
is defined recursively by the following statements:
- .
- .
- , .

- 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 numbers in modulo . - means that has the following properties:
- .

Gregory Stoll 2000-04-08