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

Vipawadee Moonchaisook


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        <foaf:name>Vipawadee Moonchaisook</foaf:name>
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            <foaf:name>, Department of Mathematics, Faculty of Science and Technology Surindra Rajabhat University, Surin, Thailand.</foaf:name>
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    <dct:title>On the Solutions of Diophantine Equation (Mp − 2) x + (Mp + 2) y = z 2 where Mp is Mersenne Prime</dct:title>
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    <dcat:keyword>Diophantine equations, exponential equations.</dcat:keyword>
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    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-08-30</dct:issued>
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    <dct:description>&lt;p&gt;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 &amp;minus; 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.&amp;nbsp;&lt;/p&gt;</dct:description>
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