Khachaturyan. $A . B$.

Natural numbers from 1 to 2014 were somehow divided into pairs, the numbers in each pair were added, and the 1007 sums obtained were multiplied.

Could the result have been a square of a natural number?
By pairing the numbers from 7 to 2014 as $\{7,2014\},\{8,2013\}, \ldots .,\{1010,1011\}$, we obtain an even number of pairs with a sum of 2021. The numbers from 1 to 6 can be paired as follows: $\{1,5\},\{2,4\},\{3,6\}$. As a result, we get the product $6^{2} \cdot 9=18^{2}$.

## Answer

Can.
