On the Diophantine Equation Mxp + (Mq + 1)y = z2
| creativework.keywords | Diophantine equation, Exponential Diophantine equation, Mersenne primes | |
| dc.contributor.author | Gayo, William S., Jr. | |
| dc.contributor.author | Bacani, Jerico B. | |
| dc.date.accessioned | 2026-08-19T05:01:25Z | |
| dc.date.available | 2026-08-19T05:01:25Z | |
| dc.date.issued | 2021 | |
| dc.description | Full text | |
| dc.description.abstract | In this paper, we study and solve the exponential Diophantine equation of the form Mxp + (Mq + 1)y = z2 for Mersenne primes Mp and Mq and non-negative integers x, y, and z. We use elementary methods, such as the factoring method and the modular arithmetic method, to prove our research results. Several illustrations are presented, as well as cases where solutions to the Diophantine equation do not exist. | |
| dc.identifier.citation | Gayo, W. S., Jr., & Bacani, J. B. (2021). On the diophantine equation Mxp+ (Mq+ 1)y = z2. European Journal of Pure and Applied Mathematics, 14(2), 396-403. https://doi.org/10.29020/nybg.ejpam.v14i2.3948 | |
| dc.identifier.doi | https://doi.org/10.29020/nybg.ejpam.v14i2.3948 | |
| dc.identifier.issn | 1307-5543 | |
| dc.identifier.uri | https://lakasa.dmmmsu.edu.ph/handle/123456789/2385 | |
| dc.language.iso | en | |
| dc.publisher | European Journal of Pure and Applied Mathematics | |
| dc.sdg | SDG 4 | |
| dc.subject | Mathematics | |
| dc.subject | Algebra | |
| dc.subject.ddc | Number theory | |
| dc.subject.lcsh | Diophantine equations | |
| dc.subject.lcsh | Numbers, Prime | |
| dc.subject.lcsh | Modular arithmetic | |
| dc.title | On the Diophantine Equation Mxp + (Mq + 1)y = z2 | |
| dc.type | Article | |
| dcterms.accessRights | Open access | |
| oaire.citation.endPage | 403 | |
| oaire.citation.issue | 2 | |
| oaire.citation.startPage | 396 | |
| oaire.citation.volume | 14 |