4. A positive integer, if added to 100 and 168 respectively, can result in two perfect squares. This positive integer is $\qquad$
4. $n=156$.

Let this number be $n$, and $n+168=a^{2}, n+100=b^{2}$. Then $a^{2}-b^{2}=68=2^{2} \times 17$,
which means $(a+b)(a-b)=2^{2} \times 17$.
However, $a+b$ and $a-b$ have the same parity,
so $a+b=34, a-b=2$.
Thus, $a=18$, and hence $n=156$.