The least period of the ratio sequence (Q2883389)

From the introduction: In their paper [Fibonacci Q. 44, No. 2, 103--108 (2006; Zbl 1165.11017)] the authors used matrix techniques and group theory to study linear recurring sequences of order \(k\geq 2\) over finite fields. One of the results in that paper on the least period of the ratio sequence has a very short proof suggested to them by L. Somer. In the present paper the authors give their original proof of this result.