Determinants Containing Powers of Generalized Fibonacci Numbers

Abstract: We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally, we discuss the determinants of matrices whose entries are products of the generalized Fibonacci numbers.