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Integers

### A note on the representability of quaternary quadratic forms as sums of squares of two linear forms

Portugaliae mathematica

Acta Arithmetica

### Algorithme de multiplicativité des sommes de carrés

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

### An arithmetic formula of Liouville

Journal de Théorie des Nombres de Bordeaux

An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.

Acta Arithmetica

Integers

### Antieigenvalue analysis for continuum mechanics, economics, and number theory

Special Matrices

My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...

### Arithmetical equivalents for a remarkable identity between theta functions . . . . . . . . . . . . . . .

Mathematische Zeitschrift

Acta Arithmetica

### Blocks for symmetric groups and their covering groups and quadratic forms.

Beiträge zur Algebra und Geometrie

Acta Arithmetica

### Congruences for ${q}^{\left[p/8\right]}\left(modp\right)$

Acta Arithmetica

Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of the integers m and n. Let p ≡ 1 (mod 4) be a prime, q ∈ ℤ, 2 ∤ q and p=c²+d²=x²+qy² with c,d,x,y ∈ ℤ and c ≡ 1 (mod 4). Suppose that (c,x+d)=1 or (d,x+c) is a power of 2. In this paper, by using the quartic reciprocity law, we determine ${q}^{\left[p/8\right]}\left(modp\right)$ in terms of c,d,x and y, where [·] is the greatest integer function. Hence we partially solve some conjectures posed in our previous two papers.

### Construction of entire modular forms of weights 5 and 6 for the congruence group ${\text{Γ}}_{0}\left(4N\right)$.

Georgian Mathematical Journal

Acta Arithmetica

### Cyclic polygons of integer points

Acta Arithmetica

Mathematische Zeitschrift

### Démonstration élémentaire d'un théorème énoncé par M. E. Catalan

Bulletin de la Société Mathématique de France

### Développements nouveaux sur quelques propositions de Fermat

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

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