Task 1. Find two consecutive natural numbers whose difference of squares is 111.
Solution. Let's denote the consecutive natural numbers by n and $n+1$. Then, from the condition we have:

$$
(n+1)^{2}-n^{2}=111, n^{2}+2 n+1-n^{2}=111,2 n=110
$$

i.e., $n=55$. Therefore, the required numbers are 55 and 56.