194. Parallel Resistors. If we connect two conductors in parallel, with resistances equal to $x$ and $y$ respectively, the resistance $z$ of such a segment can be found from the relation

$$
\frac{1}{z}=\frac{1}{x}+\frac{1}{y} ; \quad x, \quad y, \quad z>0
$$

Find positive integers $x, y, z$ that satisfy this relation.
194. Since $x, y, z$ are positive, $x>z$ and $y>z$. Let $x=$ $z+u$, and $y=z+v ; u, v>0$. The equation $\frac{1}{z}=\frac{1}{x}+\frac{1}{y}$ reduces to $z^{2}=u v$. Therefore, for any $z$, we need only factor $z^{2}$ into the product of two positive integers $w$ and $v$.

[Marion L. Gains, N. M. M., 19, 100 (November 1944).]