16. $2.29{ }^{\star \star} N$ is an integer, its base $b$ representation is 777. Find the smallest positive integer $b$, such that $N$ is a fourth power of an integer.
Let $b$ be the smallest positive integer to be found, then $7 b^{2}+7 b+7=x^{4}$. Since $7 \mid x$, let $x=7 k$, $k \in \mathbf{N}$, we have $b^{2}+b+1=7^{3} k^{4}$. When $k=1$, $(b-18)(b+19)=0$. Therefore, $b=18$ is the smallest positive integer that satisfies the condition.