The Discriminant of the Characteristic Polynomial of the kth Fibonacci sequence is not a member of the kth Lucas sequence

Key Points

• The discriminant of the characteristic polynomial is shown to be absent in the k-th Lucas sequence.
• The analysis focuses on the properties of k-generalized Lucas numbers defined as a sum of previous terms.
• Lucas numbers, beginning with terms 0,0,...,2,1, reveal unique characteristics compared to Fibonacci numbers.
• This finding highlights a distinct separation between the properties of Fibonacci and Lucas sequences.