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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 c023-math-001 if and only if c023-math-002; that is, c023-math-003 if and only if c023-math-004. In particular, c023-math-005 if and only if c023-math-006. Thus, beginning with c023-math-007, every fifth Fibonacci number is divisible by 5, a fact we already knew.

Furthermore, c023-math-008 if and only if c023-math-009; that is, if and only if . Thus,

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