(a) Give an example of a group which is abelian but not cyclic.
K4 right?
(b) Find 2^2005 in (non-zero elements)
(c) Find all solutions to the equation
Yes.
thus by raising exponents to . It remains to compute thus .(b) Find 2^2005 in (non-zero elements)
First it makes no sense to talk about negative exponents. Thus, we will solve this equation for . Any can be written as where . Thus, .(c) Find all solutions to the equation
Thus, we require that for . Direct computation shows that is the only such exponent. Thus all the solutions have the form which can be writen as for .