1985 Putnam A4

Define a sequence $\{a_i\}$ by $a_1=3$ and $a_{i+1}=3^{a_i}$ for

$i\geq 1$. Which integers between 00 and 99 inclusive occur as the

last two digits in the decimal expansion of infinitely many $a_i$?

通过 $a_1=3$ 和 $a_{i+1}=3^{a_i}$ 定义序列 $\{a_i\}$

$i\geq 1$。 00 到 99 之间的哪些整数作为

无限多个 $a_i$ 的十进制展开式的最后两位数字？