How one expect the possible values of $(x, y, z) = (0, 0,0), (1, 1, 1)$ and $(3, 1, 5)$ of the equation $3^x -2^y = z^2$ without by inspection.
Why $n = 1$ and $3$ are valid for $5^n - 4 = z^2$.
Is there any other $n$, other than these $1$ and $3$? without inspection how we prove the solutions/how we will find other solutions if there?
Prema