76. The famous Chinese mathematician, Academician Wang Yuan, once inscribed "Mathematics Competition is Good". If "数", "学", "竞", "赛", and "好" each represent a natural number from 0 to 9, and satisfy the equation "数学竞赛好 $=$ 数学 $\times$ 竞赛好 $\times 2$". Find the five-digit number represented by "数学竟赛好".
Answer: 13520, 63504.
Solution: Let mathematics $=x$, competition good $=y$, then from the given conditions, we get the equation,

That is
$$
\begin{array}{l}
1000 x+y=2 x y, \\
y=\frac{1000 x}{2 x-1} .
\end{array}
$$

This equation indicates that $2 x-1$ is a positive divisor of 1000,

Noting that
$$
1000=2^{3} \times 5^{3},
$$

and since
$2 x-1$ is an odd number, and $x$ is a two-digit number,

Therefore,
$$
2 x-1=25 \text { or } 125 \text {, }
$$

Solving for $x$ gives
$$
x=13 \text { or } 63 \text {, }
$$

Thus,
$y=520$ or 504,

Hence, the required five-digit numbers are 13520 or 63504.