【摘 要】
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Let ξ be an irrational number with simple continued fraction expansion ξ= [a0;a1,… ,ai,…] and pi/qi be its ith convergent. Let Ci be defined by ξ - pi/qi =
【机 构】
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Department of Mathematics and Statistics
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Let ξ be an irrational number with simple continued fraction expansion ξ= [a0;a1,… ,ai,…] and pi/qi be its ith convergent. Let Ci be defined by ξ - pi/qi = (-1)i/(Ciqiqi+1). The author proves the following theorem: Theorem. Let r ＞ 1, R ＞ 1 be two real numbers and L=1/r-1+1/R-1 +annan+1rR, K=1/2(L+ L2-4/(r-1)(R-1)). Then (i) Cn-2 ＜r, Cn ＜R imply Cn-1 ＞K; (ii) Cn-2 ＞r, Cn ＞R imply Cn-1 ＜K. This theorem generalizes the main result in [1].
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