Some Properties of Fibonacci Numbers
نویسندگان
چکیده
We formalized some basic properties of the Fibonacci numbers using definitions and lemmas from [7] and [23], e.g. Cassini’s and Catalan’s identities. We also showed the connections between Fibonacci numbers and Pythagorean triples as defined in [31]. The main result of this article is a proof of Carmichael’s Theorem on prime divisors of prime-generated Fibonacci numbers. According to it, if we look at the prime factors of a Fibonacci number generated by a prime number, none of them have appeared as a factor in any earlier Fibonacci number. We plan to develop the full proof of the Carmichael Theorem following [33].
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