由 danny 於 星期四 七月 25, 2013 8:03 am
w^7=1
w+w^2+w^4=k ...... (1)
(1)*w^6 => 1+w^8+w^10=k*w^6 => 1+w+w^3=k*w^6 ...... (2)
(1)*w^5 => w^6+1+w^9=k*w^5 => 1+w^2+w^6=k*w^5 ...... (3)
(1)*w^3 => w^4+w^5+1=k*w^3 => 1+w^5+w^4=k*w^3 ...... (4)
(2)+(3)+(4) => 3+w+w^2+......+w^6=k*(w^3+w^5+w^6) ...... (5)
0=w^7-1=(w-1)(1+w+w^2+......+w^6) => 1+w+w^2+......+w^6=0
so (5) => 2=k*(w^3+w^5+w^6) => w^3+w^5+w^6=2/k ... (6)
1+[(1)+(6)] => 1+[w+w^2+......+w^6]=1+[k+2/k] => 0=1+k+2/k
k=(-1±i√ 7)/2