Sums of Numbers with Small Partial Quoti
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S. Astels
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Article
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2001
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Elsevier Science
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English
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For m ยฅ Z + let F(m) be the set of numbers with an infinite continued fraction expansion where all partial quotients, except possibly the first, do not exceed m. In 1975, James Hlavka conjectured that F( )+F( ) ] R. We shall disprove Hlavka's conjecture, showing that in fact F(5) ยฑ F(2)=R.