On the Diophantine Equation Mxp + (Mq + 1)y = z2
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
European Journal of Pure and Applied Mathematics
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.
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Keywords
Mathematics, Algebra
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