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On the Completeness of the Lucas Sequence

The Fibonacci Quarterly, 1969
A sequence of positive integers is said to be complete if every positive integer is the sum of a finite number of distinct terms of the sequence. It is well-known that the Lucas sequence \(\{L_j\}\) where \(L_{n+1}=L_n+L_{n-1}\) for \(n>1\) and \(L_0=2\), \(L_1=1\) is complete. In this paper the author proves that if any term \(L_n\), where \(n>1\), is
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On k-Lucas sequences

AIP Conference Proceedings, 2014
For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
Jye-Ying Sia, C. K. Ho, Chin-Yoon Chong
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Lucas Sequences in Primality Testing

2014
Prime or composite? This classification determines whether or not integers can be used in digital security. One such way to begin testing an integers primality is with the Fermat test, which says that if n is a prime number and a is an integer then an-1 1 mod n.
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