On the Diophantine Equation Mpx

被引：7
|
作者：
Gayo, William S., Jr. [1 ,2 ]
Bacani, Jerico B. [1 ]
机构：
[1] Univ Philippines Baguio, Coll Sci, Dept Math & Comp Sci, Baguio 2600, Benguet, Philippines
[2] Don Mariano Marcos Mem State Univ North La Union, Coll Arts & Sci, Gen Educ Dept, Bacnotan 2515, La Union, Philippines
来源：
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2021年 / 14卷 / 02期
关键词：
Diophantine equation; Exponential Diophantine equation; Mersenne primes;
D O I：
10.29020/nybg.ejpam.v14i2.3948
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study and solve the exponential Diophantine equation of the form M-p(x) + (M-q + 1)(y) = z(2) for Mersenne primes M-p and M-q 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.
引用
收藏
页码：396 / 403
页数：8
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