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 Oct7 awarded Popular Question Apr30 accepted The roots of $t^5+1$ Apr29 awarded Commentator Apr29 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)? Apr29 asked The roots of $t^5+1$ Apr26 asked Ramsey theory - colouring of edges Apr22 comment Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$ Of course..! Thank you for the point out :) Apr22 asked Factorisation of a polynomial over $\mathbb Q(i,\sqrt 5)$ Apr21 accepted Irreducible Polynomial over $\mathbb{Q}$ Apr20 awarded Scholar Apr20 accepted Irreducibility of polynomials Apr20 revised Irreducible Polynomial over $\mathbb{Q}$ edited body Apr20 comment Irreducibility of polynomials Thanks for the clarification, I understand the use of the primitive cube root of unity now :) Apr20 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? Apr20 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. Apr20 asked Irreducible Polynomial over $\mathbb{Q}$ Apr20 awarded Supporter Apr20 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. Apr20 comment Irreducibility of polynomials It can be expressed as such, yes. I think I understand your meaning, thank you :) Apr20 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.