Recent content by nhartung

Nevermind. I resolved this issue. Apparently you need to call the BufferedWriter's flush() member. Strange that it was working in certain scenarios though.

Homework Statement I've implemented RSA and just need to print some stats and write to files.Homework Equations My solution works fine when I provide an input file, however, if I let it read from standard input there is no output written to either of my output files. Reading works regardless. I...

Thanks a lot, you and micromass have both helped me out immensely this semester. This is my last problem set this semester so hopefully I won't be back.

Aha! I think I have it now. We know D(1) = 0. We also know 1 can be written as the product of any n and it's inverse 1/n. (Every n but 0 has an inverse here since this is a field). With this we can prove that the derivative of any rational number is 0 as follows: 1 = (4 * 1/4) = D(1) = D(4 *...

Alright a new question here: For F a field, define the derivative map D: F[x] --> F[x] as the unique function with the following properties: D(a + b) = D(a) + D(b) D(a * b) = [D(a) * b] + [a * D(b)] and D(x) = 1. My professor also added F must be Z/p (p a prime) and F = Q (the...

Ah, I didn't see that. That should make life easier. Thanks

This must be some theorem we haven't learned yet. In class I remember my professor specifically saying that we need to check these by creating a multiplication table and checking for inverses. However, if what you said is true, I've determined that b and c must be fields because the polynomials...

Homework Statement Let F be a field, F[x] the ring of polynomials in one variable over F. For a \in F[x], let (a) be all the multiples of a in F[x] (note (a) is an ideal). If b \in F[x], let c(b) be the coset of b mod (a) (that is, the set of all b + qa, where q \in F[x]). F[x]/(a), then is the...

ok part c asks: Demonstrate that {1,11} in G_15 is a subgroup of G_15, and {1,11} in G_30 is a subgroup of G_30. Find the cosets of {1,11} in each of the groups. Part b had me find G_30 and if it was isomorphic to G_15. From that I found G_30 = {1, 7, 11, 13, 17, 19, 23, 29} which is also...

Ah, I like that proof a lot better. Thanks for the quick response, if I have any questions of the other parts of this question (didn't post them yet) i'll post them here.

Homework Statement Remember, the set of groups (Gn, *), the group of multiplicatively-invertible elements of Z/n under multiplication. For p a prime, the elements of Gp are all elements of Z/p except 0; for n not a prime, the elements of Gn are all the elements of Z/n except 0 and those...

When checking if my assumptions hold true I should also check them with the a and b values flipped to check the ab = ba assumption, I won't write them out here but I know they hold, just assume I wrote them up there.

Ok my professor did an example of groups of order 8 in my last lecture which helped a lot so I think I have it figured out now: Groups of order 9: Let G be a group of order 9, every element has order 1, 3, or 9. If there is an element g of order 9, then <g> = G. G is isomorphic to Z/9...

The group of order 4 uses the theorem that if the square of every element in the group = e then the group is Abelian which I can't use for groups of order 9. I did find an example in my book for groups of order 6 which includes an element of order 3. I'll take a look at this

Yeah I was just thinking about that, I'm a little stuck on it. I can't assume this group is abelian can I? That would make for a pretty simple proof. Otherwise I guess I can try to use some sort of associativity proof. Suppose (ab)a ≠ a2b = (ab)a ≠ a(ab) = a ≠ a (this is actually true a = a)...