On a Theorem of Nathanson on Diophantine Approximation

Abstract

In 1974, M. B. Nathanson proved that every irrational number α represented by a simple continued fraction with infinitely many elements greater than or equal to k is approximable by an infinite number of rational numbers p/q satisfying |α-p/q|<1/(k2+4q2). In this paper we refine this result.

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