33. To answer the question: "Is the difference $9^{1986}-8^{1980}$ divisible by 5 and by 10?" - one could call upon a computer. But perhaps you would like to compete with it? Give it a try.
33. Since $9^{1}=9, 9^{2}=81, 9^{3}=729$, it is clear that the odd powers of nine end in the digit 9, and the even powers end in the digit 1. Let's consider the powers of the number 8: $8^{1}=8 ; 8^{2}=64$-ends in the digit $4 ; 8^{3}$ ends in the digit $2 ; 8^{4}$ ends in the digit $6 ; 8^{5}$ ends in the digit 8, and so on. Thus, we have a repeating group of digits $8,4,2$ and 6, which are the last digits of the powers of 8. Since 1980 is divisible by 4, $8^{1980}$ ends in the digit 6, and therefore, the given difference ends in the digit 5. Hence, it is divisible by 5, but not by 10.