### Journals Information

**
Mathematics and Statistics Vol. 10(2), pp. 442 - 453 DOI: 10.13189/ms.2022.100220 Reprint (PDF) (371Kb) **

## Some Results on Number Theory and Analysis

**B. M. Cerna Maguiña ^{1}, Dik D. Lujerio Garcia ^{1}^{,*}, Héctor F. Maguiña ^{2}, Miguel A. Tarazona Giraldo ^{3}**

^{1}Academic Department of Mathematics, Science Faculty, Santiago Antúnez de Mayolo National University, Shancayan Campus, Perú

^{2}National University of San Marcos, Street Germán Amézaga N°375. Pabellón ”F”-Accounting Sciences University City, Perú

^{3}Faculty of Electronic and Computer Engineering, Federico Villarreal National University, Perú

**ABSTRACT**

In this work, we obtain bounds for the sum of the integer solutions of quadratic polynomials of two variables of the form where is a given natural number that ends in one. This allows us to decide the primality of a natural number that ends in one. Also we get some results on twin prime numbers. In addition, we use special linear functionals defined on a real Hilbert space of dimension , in which the relation is obtained: , where is a real number for . When or , we manage to address Fermat's Last Theorem and the equation , proving that both equations do not have positive integer solutions. For , the Cauchy-Schwartz Theorem and Young's inequality were proved in an original way.

**KEYWORDS**

Diophantine Equation, Prime Numbers, Twin Prime Numbers, Cauchy-Shwarz Inequality, Fermat's Last Theorem

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] B. M. Cerna Maguiña , Dik D. Lujerio Garcia , Héctor F. Maguiña , Miguel A. Tarazona Giraldo , "Some Results on Number Theory and Analysis," Mathematics and Statistics, Vol. 10, No. 2, pp. 442 - 453, 2022. DOI: 10.13189/ms.2022.100220.

(b). APA Format:

B. M. Cerna Maguiña , Dik D. Lujerio Garcia , Héctor F. Maguiña , Miguel A. Tarazona Giraldo (2022). Some Results on Number Theory and Analysis. Mathematics and Statistics, 10(2), 442 - 453. DOI: 10.13189/ms.2022.100220.