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Halfway to a solution of X 2 - D Y 2 = - 3

R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)

Journal de théorie des nombres de Bordeaux

It is well known that the continued fraction expansion of D readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of x 2 - D y 2 = ± 1 . Here we notice that, analogously, the point halfway to a solution of x 2 - D y 2 = - 3 can be recognised. We explain what is going on.

Hierarchical residue number systems with small moduli and simple converters

Tadeusz Tomczak (2011)

International Journal of Applied Mathematics and Computer Science

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k-1, 2k, 2k+1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the...

Hurwitz continued fractions with confluent hypergeometric functions

Takao Komatsu (2007)

Czechoslovak Mathematical Journal

Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions 0 F 1 ( ; c ; z ) . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.

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