user29553

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	57 reputation	bio	website		visits	member for	1 year, 1 month
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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!