Find the remainder when dividing 2^2013 by 15.
*answer should be in modulo. example: find the remainder when dividing 2^100 by 21 and the answer is 2^100 = 16mod(21).*

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Gabrielle's age is two times mikhail's age. the sum of their ages is 84. what is mikhail's age?

Aclassroom is made up of 11 boys and 14 girls. the teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). if the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?