Abstract:
For every algebraic number α of degree n⩾3 there exist effective positive constants a and C such that for any rational integers q>0 and p we have
|α−pq|>Cqa−n.
We also derive an effective boundary of the type C1ma1 for the solutions of the Diophantine equation f(x,y)=m, where f is a form of degree ⩾3.
\Bibitem{Fel71}
\by N.~I.~Fel'dman
\paper An effective refinement of the exponent in Liouville's theorem
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 5
\pages 985--1002
\mathnet{http://mi.mathnet.ru/eng/im2114}
\crossref{https://doi.org/10.1070/IM1971v005n05ABEH001130}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=289418}
\zmath{https://zbmath.org/?q=an:0237.10018}
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https://doi.org/10.1070/IM1971v005n05ABEH001130
https://www.mathnet.ru/eng/im/v35/i5/p973
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