Abstract
Let x x be a real irrational number whose continued fraction has infinitely many partial quotients not less than k k . A simple proof is given that the inequality | x − p / q | > ( k 2 + 4 ) − 1 / 2 q − 2 |x - p/q| > (k^2 + 4)^{-1/2} q^{-2} has infinitely many rational solutions p / q p/q . The constant ( k 2 + 4 ) − 1 / 2 (k^2 + 4)^{-1/2} is best possible.
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