18. 1. 11 * Find all positive integer solutions \(x, y, z, t\) to the equation \(\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}+\frac{1}{t^{2}}=1\).
Obviously, the positive integers $x, y, z, \iota$ cannot have one being 1. Moreover, $x, y, z, t$ cannot have one greater than 2; otherwise, assume without loss of generality that $x \geqslant 3$, then by $y \geqslant 2, z \geqslant 2, t \geqslant 2$ we have
$$
\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}+\frac{1}{t^{2}} \leqslant \frac{1}{9}+\frac{3}{4}<1
$$

which is impossible. Therefore, it can only be that $x=y=z=t=2$. This is the unique positive integer solution to the equation.