### Journals Information

**
Mathematics and Statistics Vol. 7(3), pp. 78 - 81 DOI: 10.13189/ms.2019.070304 Reprint (PDF) (290Kb) **

## Non-existence of Solutions of Diophantine Equations of the Form

**Renz Jimwel S. Mina ^{*}, Jerico B. Bacani **

Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Philippines

**ABSTRACT**

Numerous researches have been devoted in finding the solutions , in the set of non-negative integers, of Diophantine equations of type (1), where the values p and q are fixed. In this paper, we also deal with a more generalized form, that is, equations of type (2), where n is a positive integer. We will present results that will guarantee the non-existence of solutions of such Diophantine equations in the set of positive integers. We will use the concepts of the Legendre symbol and Jacobi symbol, which were also used in the study of other types of Diophantine equations. Here, we assume that one of the exponents is odd. With these results, the problem of solving Diophantine equations of this type will become relatively easier as compared to the previous works of several authors. Moreover, we can extend the results by considering the Diophantine equations (3) in the set of positive integers.

**KEYWORDS**

Exponential Diophantine Equations, Jacobi Symbol, Legendre Symbol

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

(a). IEEE Format:

[1] Renz Jimwel S. Mina , Jerico B. Bacani , "Non-existence of Solutions of Diophantine Equations of the Form ," Mathematics and Statistics, Vol. 7, No. 3, pp. 78 - 81, 2019. DOI: 10.13189/ms.2019.070304.

(b). APA Format:

Renz Jimwel S. Mina , Jerico B. Bacani (2019). Non-existence of Solutions of Diophantine Equations of the Form . Mathematics and Statistics, 7(3), 78 - 81. DOI: 10.13189/ms.2019.070304.