On Diophantine equation n^x+(9p)^y=z^2
In this paper, we consider integer solutions (n,p,x,y,z) for the Diophantine equation n^x+(9p)^y=z^2 where n is positive, p is prime and x,y,z are non-negative. We show that this equation has no solution if n \equiv 1 \pmod{4} and p \equiv 1 \pmod{4}. Moreover, we find solutions of the Diophantine equation n^x+(9p)^y=z^2 in some cases.
Authors
- Ronnason Chinram (ORCID: https://orcid.org/0000-0002-6113-3689)
- Theerapon Buatong
Publication Details
- Journal
- International journal of mathematics and computer science
- Published
- 2025-01-01
- DOI
- https://doi.org/10.69793/ijmcs/03.2025/theerapon
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00