Open AccessOn the Diophantine Equation Mp^x + (Mq + 1)^y = z^2
Author(s) -
William Sobredo Gayo,
Jerico B. Bacani
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i2.3948
Subject(s) - diophantine equation , mathematics , mersenne prime , integer (computer science) , arithmetic , elliptic curve , exponential function , discrete mathematics , thue equation , diophantine set , pure mathematics , mathematical analysis , computer science , programming language
In this paper, we study and solve the exponential Diophantine equation of the formMxp + (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.