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On the exponential Diophantine equation <i>m<sup>x</sup> </i>+(<i>m</i>+1)<i> <sup>y</sup> </i>=(1+<i>m</i>+<i>m</i> <sup>2</sup>)<i> <sup>z</sup> </i>
Abstract Let m > 1 be a positive integer. We show that the exponential Diophantine equation m x + ( m + 1) y = (1 + m + m 2 ) z has only the positive integer solution ( x, y, z ) = (2, 1, 1) when m …