On the Solutions of Diophantine Equation (Mp− 2)x + (Mp + 2)y = z2 where Mp is Mersenne Prime
Vipawadee Moonchaisook

Vipawadee Moonchaisook*, Department of Mathematics, Faculty of Science and Technology Surindra Rajabhat University, Surin, Thailand.
Manuscript received on August 10, 2021. | Revised Manuscript received on August 22, 2021. | Manuscript published on August 30, 2021. | PP: 1-3 | Volume-3, Issue-4, August 2021. | Retrieval Number: 100.1/ijbsac.D0216063421 | DOI:10.35940/ijbsac.D0216.083421
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: The Diophantine equation has been studied by many researchers in number theory because it helps in solving variety of complicated puzzle problems. From several studies, many interesting proofs have been found. In this paper, the researcher has examined the solutions of Diophantine equation (Mp− 2)x + (Mp + 2)y = z2 where 𝑴𝒑 is a Mersenne Prime and p is an odd prime whereas x, y and z are nonnegative integers. It was found that this Diophantine equation has no solution.
Keywords: Diophantine equations, exponential equations.