A simple proof of Carmichael's theorem on primitive divisors (Q2765405)

The problem of the existence of primitive divisors for every term of a Lucas sequence is a quite famous one. After the work of many authors, its complete solution was given in a 2001 paper of \textit{Yu. Bilu, G. Hanrot} and \textit{P. M. Voutier} [J. Reine Angew. Math. 539, 75-122 (2001; Zbl 0995.11010)]. In that paper, the interested reader can find a rich relevant bibliography. The problem is very much easier when the characterisitic (second-degree) polynomial which generates the Lucas sequence has real roots, and was solved by Carmichael in 1913. In this paper the author gives another proof which is very simple.