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In this paper we prove by Model-Theoretic method that the Equation in the Title (with p a prime) is Solvable in the Ring of Square Integer Matrices of order n with n any positive integer.[J.H.E.Cohn has proved that the Diophantine Equation xp+ 1 =py2 (p a positive odd prime)has no positive integer solution [see 2003,131(1) pp13-15.]