Linear recursive sequences and factorials

Abstract

In the second chapter of this work, when discussing linear recursive sequences, many results can be read about Fibonacci numbers. We discuss theorems about recursive sequences, where the quotient of adjacent terms of the sequences approaches the golden ratio. Later, integer sequences are constructed as linear combinations of Fibonacci numbers and rational polynomials. In the last part of the chapter, we deal with the convolution of second order linear recursive sequences, where Fibonacci numbers and other famous sequences also appear. In the third chapter, we discuss the question of finding all products of factorials yielding a factorial, which is a long standing problem, studied by many authors.