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## Definitions

• 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.    Next: Theorems Up: Fibonacci-q numbers and new Previous: Fibonacci-q numbers and new   Contents
Gregory Stoll 2000-04-08