(4) If $4n+1, 6n+1$ are both perfect squares, then the smallest positive integer value of $n$ is
$\qquad$
(4) 20 Hint: $4 n+1,6 n+1$ are both odd square numbers; let
$$
6 n+1=(2 m+1)^{2}=4 m(m+1)+1 \text {, }
$$

then $3 n=2 m(m+1)$, and $m(m+1)$ is even, so $4 \mid n$, let $n=4 k$, then $4 n+1=16 k+1,6 n+1=24 k+1$, when $k=1,2,3,4$, $4 n+1$, $6 n+1$ are not both square numbers, but when $k=5$, i.e., $n=20$, $4 n+1=81,6 n+$ $1=121$ are both square numbers, therefore the smallest positive integer $n$ is 20.