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On a Diophantine Equation X^3 -1/Y^3 -1=Z^2

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Abstract: In this paper, a Diophantine equation given by Gary Walsh in an advanced workshop (May 14-16, 2007), on the solvability of Diophantine equations, held at the Lorentz Center of Leiden University, The Netherlands, is studied. The problem goes as "Are there infinitely many positive integer solutions to x^3 −1 y^3 −1 =z^2 ? "

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