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Published online by Cambridge University Press: 26 February 2010
It was proved recently by Roth that if α is any real algebraic number, and κ > 2, then the inequality
has only a finite number of solutions in integers h and q, where q > 0 and (h, q) = 1. This remarkable result answered finally a question which had been only partially answered by the work of Thue and Siegel.
page 40 note † Mathematika, 2 (1955), 1–20. This paper will be referred to as R.CrossRefGoogle Scholar
page 40 note ‡ Math. Annalen, 107 (1933), 691–730.CrossRefGoogle Scholar
page 40 note § See, for example, Waerden, van der, Moderne Algebra I (New York, 1953), 235–243.Google Scholar
page 41 note † Loc. cit., Hilfsatz 5 and §18.
page 41 note ‡ Math. Annalen, 108 (1933), 37–55.
page 47 note ‡ Mahler, lco. cit., 701.