Generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2

Abstract: Using the properties of generalized Fibonacci numbers, we determine the automorphism groups of some K3 surfaces with Picard number 2. Conversely, using the automorphisms of K3 surfaces with Picard number 2, we prove the criterion for a given integer n is to be a generalized Fibonacci number. Moreover, we show that the generalized k-th Fibonacci number divides the generalized q-th Fibonacci number if and only if k divides q.