Let's decide which of the following two numbers is larger:

$$
\frac{7}{5 \cdot 9150625}-\frac{1}{605 \cdot 125^{2}} \text { and } \frac{1}{\left(123^{2}-4\right) \cdot 1375}
$$
Let the first number be denoted by $A$ and the second number by $B$.

$$
\begin{gathered}
A=\frac{7}{5 \cdot 5^{4} \cdot 11^{4}}-\frac{1}{5 \cdot 11^{2} \cdot 5^{6}}=\frac{7}{5^{5} \cdot 11^{4}}-\frac{1}{5^{7} \cdot 11^{2}}=\frac{7 \cdot 5^{2}-11^{2}}{5^{7} \cdot 11^{4}}= \\
=\frac{175-121}{5^{7} \cdot 11^{4}}=\frac{54}{5^{7} \cdot 11^{4}}, \\
B=\frac{1}{(123+2)(123-2) 5^{3} \cdot 11}=\frac{1}{125 \cdot 121 \cdot 5^{3} \cdot 11}=\frac{1}{5^{6} \cdot 11^{3}}= \\
=\frac{5 \cdot 11}{5^{7} \cdot 11^{4}}=\frac{55}{5^{7} \cdot 11^{4}} .
\end{gathered}
$$

Therefore, $B>A$.

Tibor Harza (Székesfehérvár, József Attila g. I. o. t.)