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seen May 30 '12 at 11:07

Apr
30
accepted The roots of $t^5+1$
Apr
29
awarded  Commentator
Apr
29
comment The roots of $t^5+1$
@CliveNewstead, so the roots are -1, -w, -w^2, -w^3, -w^4, with w=e^(2ipi/5)?
Apr
29
asked The roots of $t^5+1$
Apr
26
asked Ramsey theory - colouring of edges
Apr
22
comment Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$
Of course..! Thank you for the point out :)
Apr
22
asked Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$
Apr
21
accepted Irreducible Polynomial over $\mathbb{Q}$
Apr
20
awarded  Scholar
Apr
20
accepted Irreducibility of polynomials
Apr
20
revised Irreducible Polynomial over $\mathbb{Q}$
edited body
Apr
20
comment Irreducibility of polynomials
Thanks for the clarification, I understand the use of the primitive cube root of unity now :)
Apr
20
comment Irreducible Polynomial over $\mathbb{Q}$
Thank you, Martin, this has helped a lot! Is there a way to achieve this result without looking at the poly in Z2?
Apr
20
comment Irreducible Polynomial over $\mathbb{Q}$
Thank you! I would not have come across using Gauss's theorem of primitive polynomials unless after many hours! So, can we use this for any primitive polynomial, i.e. can we use this principle to find the factorisation of g(x), a primitive cubic poly? Many thanks.
Apr
20
asked Irreducible Polynomial over $\mathbb{Q}$
Apr
20
awarded  Supporter
Apr
20
comment Irreducibility of polynomials
Hi there, thank you for such a wonderfully detailed explanation, it was extremely helpful! I was wondering, should the quadratic in Z5 read (x^2+3x+4) rather than (x^2+2x+4)? And hence the discriminant be 9-16=-7 congruent to 3 mod 5? Also, as for the complex factorisation, could you please explain to me why we are going about it by introducing the primitive root of unity (I understand what the primitive root of unity is, etc.)? Thank you.
Apr
20
comment Irreducibility of polynomials
It can be expressed as such, yes. I think I understand your meaning, thank you :)
Apr
20
comment Irreducibility of polynomials
Btw, I now understand how we can factorise this into irreducibles over R, but what about C? If there is no imaginary part, is it still a valid factorisation in C? Sorry if that is too basic a question.
Apr
20
comment Irreducibility of polynomials
Thank you for explaining this!