### Journals Information

**
Mathematics and Statistics Vol. 10(5), pp. 1005 - 1013 DOI: 10.13189/ms.2022.100512 Reprint (PDF) (318Kb) **

## Some Results on Theory of Numbers, Partial Differential Equations and Numerical Analysis

**B. M. Cerna Maguiña ^{1}^{,*}, Dik D. Lujerio Garcia ^{1}, Carlos Reyes Pareja ^{1}, Torres Dominguez Cinthia ^{2}**

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

^{2}Academic Department of Civil Engineering, Santiago Antúnez de Mayolo National University, Peru

**ABSTRACT**

In this article, given a number that ends in one and assuming that there are integer solutions for the equations or or , the straight line was used passing through the center of gravity of the triangle bounded by the vertices . Considering A ≥ 25, we manage to divide the domain of the curve into two disjoint subsets, and using Theorem (2.2) of this article, we find the subset where the integer solution of the equation is found. Similar process is done when , in case P is of the form or . These curves are different and to obtain a process similar to the one carried out previously, we proceeded according to Observation 2.2. Our results allow minimizing the number of operations to perform when our problem requires to be implemented computationally. Furthermore, we obtain some conditions to find the solution of the equations: , where is of class , and is a bounded open domain of with piecewise smooth boundary . All the operations carried out to find the solution have been carried out assuming that these exist, and we have found the conditions that must satisfy for the coefficients . We finish by finding an optimal domain for the real solution of a given polynomial of degree five. This process carried out on said given polynomial can also be carried out to reduce the degree of a given polynomial and thus obtain information about its roots.

**KEYWORDS**

Prime Numbers, Diophantine Equations, Differential Equations, Number Theory, Functional Analysis

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

(a). IEEE Format:

[1] B. M. Cerna Maguiña , Dik D. Lujerio Garcia , Carlos Reyes Pareja , Torres Dominguez Cinthia , "Some Results on Theory of Numbers, Partial Differential Equations and Numerical Analysis," Mathematics and Statistics, Vol. 10, No. 5, pp. 1005 - 1013, 2022. DOI: 10.13189/ms.2022.100512.

(b). APA Format:

B. M. Cerna Maguiña , Dik D. Lujerio Garcia , Carlos Reyes Pareja , Torres Dominguez Cinthia (2022). Some Results on Theory of Numbers, Partial Differential Equations and Numerical Analysis. Mathematics and Statistics, 10(5), 1005 - 1013. DOI: 10.13189/ms.2022.100512.