相关论文: Ley de Reciprocidad Cuadr\'atica y aplicaciones

A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.

Prime numbers play a key role in number theory and have applications beyond Mathematics. In particular, in the Theory of Codes and also in Cryptography, the properties of prime numbers are relevant, because, from them, it is possible to…

This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…

In this note we will present a supplement to Scholz's reciprocity law and discuss applications to the structure of 2-class groups of quadratic number fields.

The Law of Quadratic Reciprocity was conjectured by Euler and Legendre who both found an incomplete proof. Gauss called this law "Theorema Fundamentale", and he was the first who gave a complete proof, he also highlighted the equivalence of…

We present a creative reimagining of Zolotarev's classical proof of the Law of Quadratic Reciprocity.

We continue investigating rational quartic reciprocity laws and, at the suggestion of the editor of AA, provide details of a proof of a remark in the first article with this title.

The determinant of a skew-symmetric matrix has a canonical square root given by the Pfaffian. Similarly, the resultant of two reciprocal polynomials of even degree has a canonical square root given by their reciprocant. Computing the…

This article discusses some important applications of the quadratic function with the aim of highlighting the importance of cuadr\'aticas.- forms are also intended to show how a simple function covers virtually all areas of knowledge are…

We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…

In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…

In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an…

The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…

In this article we study the 2-Selmer groups of number fields $F$ as well as some related groups, and present connections to the quadratic reciprocity law in $F$.

This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

Given the equations of the first and the second order surfaces in multidimensional space, our goal is to construct a univariate polynomial one of the zeros of which coincides with the square of the distance between these surfaces. To…

We consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special $R_{II}$ recurrence relation. We also look into some methods for generating the nodes (which lie on…