4. Find the smallest four-digit number that is equal to the square of the sum of the numbers formed by its first two digits and its last two digits.
4. Let the desired number be $N=100 a+b$, where $a$ is the number written by the first two digits of the desired number, and $b$ is the last two digits. According to the problem, $100 a+b=(a+b)^{2}$. From this equation, we express $a+b$ in terms of $a$. By trial and error, we establish that $a+b$ will be an integer when $a=20, b=25, N=2025$.