AbstractUsing known properties of continued fractions, we give a very simple and elementary proof of the theorem of Epstein and Rédei on the impossibility in a certain case of representing −1 by the quadratic form x2 − 2py2. Two of our theorems, which concern the representation of a2 and −2a2, serve to extend our method to an unknown case in which −1 is not representable
AbstractExplicit formulae are given relating continued fractions with almost periodic or almost symm...
In this dissertation we investigate prior definitions for p-adic continued fractions and introduce s...
AbstractThe continued fraction expansion and infrastructure for quadratic congruence function fields...
AbstractUsing known properties of continued fractions, we give a very simple and elementary proof of...
For primes that can be written as a sum of integer squares, p = asup2 + (2b)sup2, Kaplansky asked wh...
In this paper, we will first summarize known results concerning contin-ued fractions. Then we will l...
We explore methods for determining the underlying structure of certain classes of continued fraction...
AbstractLet m denote a positive nonsquare integer. It is shown that if Pell's equation X2 − mY2 = −1...
The solution of the quadratic equation x2-2bx+c=0 (1) with c negative is x=b1+c/x (2) where b1=2b
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
The representation of integers in binary quadratic forms has been a penchant for mathematicians thro...
AbstractUsing another approach to form approximants of the two-dimensional continued fraction, eleme...
AbstractTextIt is a theorem of Kaplansky that a prime p≡1(mod16) is representable by both or none of...
The study of arithmetical continued fractions has been restricted, for the most part, to the investi...
This article concerns the arithmetics of binary quadratic forms with integer coefficients, the De Si...
AbstractExplicit formulae are given relating continued fractions with almost periodic or almost symm...
In this dissertation we investigate prior definitions for p-adic continued fractions and introduce s...
AbstractThe continued fraction expansion and infrastructure for quadratic congruence function fields...
AbstractUsing known properties of continued fractions, we give a very simple and elementary proof of...
For primes that can be written as a sum of integer squares, p = asup2 + (2b)sup2, Kaplansky asked wh...
In this paper, we will first summarize known results concerning contin-ued fractions. Then we will l...
We explore methods for determining the underlying structure of certain classes of continued fraction...
AbstractLet m denote a positive nonsquare integer. It is shown that if Pell's equation X2 − mY2 = −1...
The solution of the quadratic equation x2-2bx+c=0 (1) with c negative is x=b1+c/x (2) where b1=2b
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
The representation of integers in binary quadratic forms has been a penchant for mathematicians thro...
AbstractUsing another approach to form approximants of the two-dimensional continued fraction, eleme...
AbstractTextIt is a theorem of Kaplansky that a prime p≡1(mod16) is representable by both or none of...
The study of arithmetical continued fractions has been restricted, for the most part, to the investi...
This article concerns the arithmetics of binary quadratic forms with integer coefficients, the De Si...
AbstractExplicit formulae are given relating continued fractions with almost periodic or almost symm...
In this dissertation we investigate prior definitions for p-adic continued fractions and introduce s...
AbstractThe continued fraction expansion and infrastructure for quadratic congruence function fields...
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