1. The sum of two integers was multiplied by their product. Could the result be 20182017?
1. Let $a \cdot b \cdot(a+b)=20182017$. Since the number 20182017 is odd, each of the factors on the left must also be odd. However, if $a$ and $b$ are odd numbers, then their sum $a+b$ is even, and the entire product $a \cdot b \cdot(a+b)$ will be even. This leads to a contradiction. Therefore, the number 20182017 could not have been obtained.

Answer: could not have.