Determining whether or not an expression is multiplicative.

Is this expression multiplicative? Justify your answer. f(n)=1, n>1. Factor n into a product of primes,n=p1^k1* p2^k2... then set f(n)= (-1)^k1+k2+...+kr.

Finding the last two digits of an exponential function.

What are the last two digits of ((9)^9)^9?

Working with congruent and incongruent solutions.

For which integers c, 0<=c<=1001, does the congruence 154x=c(mod1001) have a solution? When there are solutions how many incongruent solutions are there?

Fermat's theorem

Use Fermat's theorem to calculate the remainder when 3^1000 is divided by 7.

Finding integers that do not have primitive roots.

Find all integers larger than 19 and smaller than 31 which do not have primitive roots.