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