number theory

The digit in the unit's place of the product $3^{999} \times 7^{1000}$ is _________.

How many integers are there between 100 and 1000 all of whose digits are even?

For what values of k given below is $\frac{(k+2)^2}{k-3}$ an integer?

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X³ will have