I'm stuck on one part of a problem.
"suppose where t is odd, and for odd prime p and positive integer e.
Let L be the subgroup of false witnesses, i.e. L is the set of congruence classes made up of integers b prime to n such that
Now suppose the order of L is .
Let g be a primitive root mod n,so g has order and every element prime to n is of the form for some j.
Show that for every integer belonging to a congruence class in L, j must be even. Since |L|=t, explain why "
I really don't know what to do here so any help would be appreciated.
Are you sure you posted the problem exactly?
Sorry, the question is a little confusing, but everything I typed is correct, but I did leave a part out at the beginning,
" , suppose where s is an odd integer. Show that , where t is odd."
I think I did that part correctly. The bulk of the problem is trying to show that
Suppose it happens that .
is impossible through 3 steps, so it's kind of a guided proof by contradiction (or so i think).
1. The first step is to explain why every element of L must have odd order. I think I did this part correctly but I'm not 100% positive.
2. The next part is the question about the primitive g mod n.
3. Show that , and use that to show . Why is this impossible.
So I thought the actual contradiction comes from part three, which I haven't even gotten to yet.