Tagged Questions
1
vote
3answers
64 views
Way to show $x^n + y^n = z^n$ factorises as $(x + y)(x + \zeta y) \cdots (x + \zeta^{n-1}y) = z^n$
For odd $n$ the Fermat equation $x^n + y^n = z^n$ factorises as $$(x + y)(x + \zeta y) \cdots (x + \zeta^{n-1}y) = z^n,$$
where $\zeta = e^{2 \pi i/n}$. I tried seeing this was true by multiplying ...
-1
votes
1answer
84 views
Discriminant and roots of $ x^{n^2} \pm (x-1)^{n^2}$?
When considering the polynomials $x^{n^2} \pm (x-1)^{n^2}$ ( $n$ integer > 1 ) i noticed some things that appeared weird to me.
Discriminant($x^{n^2} + (x-1)^{n^2}) = (n^2)^{n^2}$.
...
4
votes
2answers
427 views
If z is one of the fifth roots of unity, not 1…
If z is one of the fifth roots of unity, not 1, show that:
$1+z+z^2+z^3+z^4=0$
Which wasn't too bad, but the next part is killing me: show that:
$z-z^2+z^3-z^4=2i(sin(2\pi/5)-sin(\pi/5))$
Can ...
