Endpoints of gaps in the Markoff spectrum (Q1086278)

It is proved that if the interval (a,b) is a gap in the Markoff spectrum, then the left endpoint can be written as the sum of two quadratic irrationals. This was proved earlier, with a different method, by \textit{B. Dietz} [ibid. 96, 265-267 (1983; Zbl 0517.10021)]. The paper also gives a similar result for one type of right endpoint. An earlier claim of a more general result for right endpoints by \textit{N. Davis} and \textit{J. R. Kinney} [Can. J. Math. 25, 578-584 (1973; Zbl 0276.10006)] is shown to be erroneous.