Sums of squares and orthogonal integral vectors

  title={Sums of squares and orthogonal integral vectors},
  author={Lee M. Goswick and Emil W. Kiss and G{\'a}bor Moussong and Nandor Sim{\'a}nyi},
  journal={Journal of Number Theory},

Cubes of integral vectors in dimension four

A system of $m$ nonzero vectors in $\mathbb{Z}^n$ is called an $m$-icube if they are pairwise orthogonal and have the same length. The paper describes $m$-icubes in $\mathbb{Z}^4$ for $2\le m\le 4$

Cubic sublattices

A sublattice of the three-dimensional integer lattice Z is called cubic sublattice if there exists a basis of the sublattice whose elements are pairwise orthogonal and of equal lengths. We show that

A sum of three nonunit squares of integers

We say a positive integer is a sum of three nonunit squares if it is a sum of three squares of integers other than one. In this article, we find all integers which are sums of three nonunit squares

Ehrhart polynomial for lattice squares, cubes and hypercubes

For squares and cubes and hypercubes, the Ehrhart polynomial is found, one of the coefficients is computed and there exists a simple linear relation between the other two unknown coefficients.

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My Numbers, My Friends: Popular Lectures on Number Theory

The Fibonacci Numbers and the Arctic Ocean.- Representation of Real Numbers by Means of Fibonacci Numbers.- Prime Number Records.- Selling Primes.- Euler's Famous Prime Generating Polynomial and the

On Quaternions and Octonions

This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional

On the Representations of xy + yz + ZX

It is shown that there are at most 19 integers that are not of the form xy + yz + xz with x, y, z ≥ 1 and the remaining possibility must be greater than 1011 and cannot occur if the Generalized Riemann Hypothesis is assumed.

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1 Preliminaries.- 1. The Problems of Representations and Their Solutions.- 2. Methods.- 3. The Contents of This Book.- 4. References.- 5. Problems.- 6. Notation.- 2 Sums of Two Squares.- 1. The One

An Introduction to the Theory of Numbers

  • E. T.
  • Mathematics
  • 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.

The University of Alabama at Birmingham.

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Arithmetic of Quaternions

Vorlesungen über die Zahlentheorie der Quaternionen