Aye aye. Local bookshop only stocks stuff that are usable for just maths, not so much for FM ;-;
There used to be a school website who had them all, the website is no longer up, I've got the livetext for each book but none that are just the PDF themselves
There used to be a school website who had them all, the website is no longer up, I've got the livetext for each book but none that are just the PDF themselves
Doesn't make sense, there isn't really a thing as a principal root for n-th roots where n>2 in the complexes, so for example, the LHS has 4 fourth roots whilst the RHS has 3 third roots and you're claiming the two are equivalent.
Doesn't make sense, there isn't really a thing as a principal root for n-th roots where n>2 in the complexes, so for example, the LHS has 4 fourth roots whilst the RHS has 3 third roots and you're claiming the two are equivalent.
I've tried to edit it because it's not fully what I mean to put. I will try and edit it in a minute again.
That's still straight forward. Maybe it's just me, never had a problem with roots of unity in FM. The only thing to do here is to convert it into reiθ form, factor out indices and maybe draw yourself a complex plane so there isn't much challenge.
That's still straight forward. Maybe it's just me, never had a problem with roots of unity in FM. The only thing to do here is to convert it into reiθ form so there isn't much challenge.
I just play around with a few concepts and see if I can make any interesting questions from it. Obviously not here.
Bleurgh, no. All these are boring and tedious questions. For a given complex number a, call a a primitive nth root of unity if and only if an=1 and there is no integer m such that am=1 where 0<m<n.
Let Cn(x) be the (cyclotomic) polynomial such that the roots of the equations of Cn are the primitive nth roots of unity, the coefficient of the highest power of x is 1 and all roots have multiplicity 1.
Find Cp(x) where p is a given prime and prove that there are no positive integers q,r and s such that Cq(x)≡Cr(x)Cs(x).
Bleurgh, no. All these are boring and tedious questions. For a given complex number a, call a a primitive nth root of unity if and only if an=1 and there is no integer m such that am=1 where 0<m<n.
Let Cn(x) be the (cyclotomic) polynomial such that the roots of the equations of Cn are the primitive nth roots of unity, the coefficient of the highest power of x is 1 and all roots have multiplicity 1.
Find Cp(x) where p is a given prime and prove that there are no positive integers q,r and s such that Cq(x)≡Cr(x)Cs(x).
No thanks. I don't think many Y13's will know what to do here lol