Titlebook: Solving the Pell Equation; Michael J. Jacobson,Hugh C. Williams Textbook 20091st edition Springer-Verlag New York 2009 algebra.algebraic n

关节炎

CHURL

Some Additional Analytic Results,llary 8.35.1 for determining ., we notice that the expression for .(1, χΔ) is an infinite series. The purpose of this section is to derive a closed-form formula for .. To this end we must first consider some properties of a particular Gauss sum.

一加就喷出

圣歌

Compact Representations,ould not be possible to write them out in conventional decimal representation. Indeed, it is clear that the problem of doing so is of exponential complexity in .. For example, at the end of §3.3 we mentioned the 30-digit .. By using the ideas mentioned in Chapter 10, it was shown. that ..

GLOOM

Applications to Cryptography,utation and personal integrity. Thus, it is essential today, more than ever, to develop techniques that will protect our communications. One essential component of any installation in which secure communication is needed is cryptography. Its use goes back to Julius Caesar, or perhaps even earlier.

萤火虫

Introduction,h equations goes back to the ancients; indeed, they are named after Diophantus of Alexandria (c. 200–284 AD) in honour of his work on them... However, it is most likely that the Greek mathematicians were investigating their properties much earlier than this. To take a simple example, consider the eq

sorbitol

Early History of the Pell Equation,in some detail by Konen,. Whitford,., and Dickson,. our discussion here will be brief. We will concentrate on providing a more modern historical perspective and a somewhat different presentation of this material than that given in these earlier works.

Buttress

Quadratic Number Fields,will first be necessary to develop some theory of these structures. Several of the results in this section will be given without proof because they are standard elementary results which can be found in several texts.. We will begin with the definition of an algebraic number

谎言

Ideals and Continued Fractions,nding ideal class, [.], contains an infinitude of ideals. In order to deal with this difficulty in managing [.], we will restrict our attention to a finite subset of particular ideals of [.]. To this end we provide the following definitions.

Eviction