CONTINUED FRACTIONS WITH ODD PARTIAL QUOTIENTS
نویسندگان
چکیده
منابع مشابه
Continued Fractions with Partial Quotients Bounded in Average
We ask, for which n does there exists a k, 1 ≤ k < n and (k, n) = 1, so that k/n has a continued fraction whose partial quotients are bounded in average by a constant B? This question is intimately connected with several other well-known problems, and we provide a lower bound in the case of B = 2.
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Throughout this paper N is a positive integer which is not a perfect square. The continued fraction for √ N has the periodic form √ N = [a0, a1, a2, . . . , al], (1.1) where a1, a2, . . . , al−1 is a palindrome (al−1 = a1, and so on) and al = 2a0; see, for example, [2, page 104]. The period l = l(N) is assumed to be of minimal length. This paper gives several new results concerning the followin...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112500947