On the Solutions of Diophantine Equation (Mp − 2) x + (Mp + 2) y = z 2 where Mp is Mersenne Prime
- 30 August 2021
- journal article
- Published by Blue Eyes Intelligence Engineering and Sciences Engineering and Sciences Publication - BEIESP in International Journal of Basic Sciences and Applied Computing
- Vol. 3 (4), 1-3
- https://doi.org/10.35940/ijbsac.d0216.083421
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 = 𝒛 𝟐 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
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