show that $\displaystyle 11^{33}-11^{31} $ is exactly divisible by 5
You mean power of 11, not multiple of 11. Remember ordinary elementary school subtraction.. start at the units digit... so if the top number has a 1 and so does the bottom number, the difference must have 0 as units digit..... so it's a multiple of 10, as you say even and divisible by 5.