Abstract: U ovom radu definirali smo Fibonaccijeve brojeve i njihova svojstva, a također smo se upoznali i s rezultatima vezanim uz djeljivost Fibonaccijevih brojeva. Proučili smo i niz brojeva usko vezan za Fibonaccijeve brojeve, a to je Lucasov niz. Osvrnuli smo se i na neka njegova svojstva, a potom i na identitete koji povezuju Lucasove i Fibonaccijeve brojeve. Uveli smo i bitne formule za Fibonaccijeve i Lucasove brojeve, a to su Cassinijeva i Binetova formula. Pomoću Binetove formule povezali smo ova dva niza brojeva sa zlatnim rezom, a potom i brojnim pojavama u arhitekturi, umjetnosti i prirodi. ; In this paper, we defined the Fibonacci numbers and their properties. Also we familiarized ourselves with results related to the divisibility of Fibonacci numbers. We studied a sequence closely related to Fibonacci numbers, known as the Lucas sequence. We also discussed some of its properties, followed by identities connecting Lucas and Fibonacci numbers. We introduced formulas for Fibonacci and Lucas numbers were introduced, known as Cassini’s and Binet’s formulas. Through the Binet formula, we connected these two sequences of numbers with the golden ratio, and subsequently with numerous phenomena in architecture, art, and nature.
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