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

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 30 Aug 2021Publisher:Blue Eyes Intelligence Engineering and Sciences Engineering and Sciences Publication - BEIESPJournal:International Journal of Basic Sciences and Applied Computing, volume 3, pages 1-3 (eissn: 2394-367X,

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Authors: Vipawadee Moonchaisook;

doi: 10.35940/ijbsac.d0216.083421

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

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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.

Related Organizations

Surindra Rajabhat University
Thailand

Keywords

Diophantine equations, exponential equations.

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