4. Given that the sum of the sum, difference, product, and quotient of two positive integers is 2009, then these two numbers are $\qquad$
4. 246 and 6 detailed: Let the two positive integers be $a, b$, then $a+b+a-b+a b+\frac{a}{b}=2009$, from which we can infer that $a$ is a multiple of $b$. Since the left side $=2 a+a b+\frac{a}{b}=\frac{a}{b}(b+1)^{2}=2009=41 \cdot 7^{2}$. Therefore, $\frac{a}{b}=41, b+1=7$. Thus, $a=246, b=6$.