FIBONACCI AND LUCAS CONGRUENCES
We can employ the congruence relation to extract a host of Fibonacci and Lucas properties. To begin with, we will identify Fibonacci numbers ending in zero.
23.1 FIBONACCI NUMBERS ENDING IN ZERO
In Chapter 10, we found that if and only if ; that is, if and only if . In particular, if and only if . Thus, beginning with , every fifth Fibonacci number is divisible by 5, a fact we already knew.
Furthermore, if and only if ; that is, if and only if . Thus,