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In 2012, T. Miyazaki and A. Togb\'{e} gave all of the solutions of theDiophantine equations $(2am-1)^x+(2m)^y=(2am+1)^z$ and $b^x+2^y=(b+2)^z$ inpositive integers $x,y,z,$ $a>1$ and $b\ge 5$ odd. In this paper, we propose asimilar problem (which we call the shuffle variant of a Diophantine equation ofMiyazaki and Togb\'{e}). Here we first prove that the Diophantine equation$(2am+1)^x+(2m)^y=(2am-1)^z$ has only the solutions $(a, m, x, y, z)=(2, 1, 2,1, 3)$ and $(2,1,1,2,2)$ in positive integers $a>1,m,x,y,z$. Then using thisresult, we show that the Diophantine equation $b^x+2^y=(b-2)^z$ has only thesolutions $(b,x, y, z)=(5, 2, 1, 3)$ and $(5,1,2,2)$ in positive integers$x,y,z$ and $b$ odd.

The Shuffle Variant of a Diophantine equation of Miyazaki and Togb\'{e}