3. On the left half of the board, the number 21 is written, and on the right half, the number 8 is written. It is allowed to take an arbitrary number \(a\) from the left half of the board and an arbitrary number \(b\) from the right half of the board, compute the numbers \(ab\), \(a^3 + b^3\), and write \(ab\) on the left and \(a^3 + b^3\) on the right side of the board, respectively. Can the number 2013201420152016 be obtained on the board using such operations?
# Answer: No  Solution.

Note that the number $21: 7$, and 8 gives a remainder of 1. Therefore, after the first operation, the number $a b: 7$, and the number $a^{3}+b^{3}$ gives a remainder of 1 when divided by 7. Thus, we get that on the left board we will write a number divisible by 7, and on the right board a number giving a remainder of 1 when divided by 7. Consequently, after several such operations, on the left board there will be numbers divisible by 7, and on the right board numbers giving a remainder of 1, but the number 2013201420152016 gives a remainder of 3 when divided by 7.