Problem 3. Determine a finite set $M$ of consecutive natural numbers, knowing that the difference between the largest and the smallest element is 2015, and the sum of the three smallest elements of the set $M$ is 2016.
## Solution and Scoring

Let $M=\{a+1, a+2, \ldots, a+n\}$ $1 \text{p}$

We have: $(a+n)-(a+1)=2015$ and $a+1+a+2+a+3=2016$ $3 \text{p}$

We obtain $n=2016$ and $a=670$ $2 \text{p}$

The sought set is $M=\{671,672,673, \ldots, 2686\}$. $1 \text{p}$