Interesting property of Fibonacci series

When we take a look at Fibonacci series, through modulo arithmetic, we get some interesting observations :

http://www.math.temple.edu/~renault/fibonacci/fib.html
http://en.wikipedia.org/wiki/Pisano_period

Maths is interesting, because there is so much beauty to discover.

partha

PS: This was a question in my exam for Kathmandu Uiniversity students.