Abstract
This chapter explores a few divisibility properties of Fibonacci and Lucas numbers. It discuses a theorem which shows that the greatest common divisor (GCD) of two Fibonacci numbers is also a Fibonacci number. Its proof uses the Euclidean algorithm. In 1965, M. Wunderlich of the University of Colorado employed the theorem to provide a beautiful proof that there are infinitely many primes, a fact that is universally known. A quick look at Lucas numbers shows that every third Lucas number is even.
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