1)This problem is for the younger kids give them a chance, please. Let $\displaystyle A,B$ be randomly chosen from $\displaystyle \{ 1,2,...,2007 \}$ (they can be the same). What is the probability that it is possible to find tworealnumbers that have their product equal to $\displaystyle A$ and their sum equal to $\displaystyle B$. (By the way, "real", means non-imaginary).

2)Let $\displaystyle f(x),g(x)$ be continous on $\displaystyle [0,1]$ so that $\displaystyle \int_0^1 x^n f(x) dx = \int_0^1 x^n g(x) dx$ for all $\displaystyle n\geq 0$. Prove that $\displaystyle f(x) = g(x)$. (This is a classic).