Journal article Open Access

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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    <subfield code="a">Diophantine equations, exponential equations.</subfield>
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    <subfield code="u">, Department of Mathematics, Faculty of Science and Technology Surindra Rajabhat University, Surin, Thailand.</subfield>
    <subfield code="a">Vipawadee Moonchaisook</subfield>
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    <subfield code="a">On the Solutions of Diophantine Equation (Mp − 2) x + (Mp + 2) y = z 2 where Mp is Mersenne Prime</subfield>
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    <subfield code="a">&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;</subfield>
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