α=cos2π/5+isin2π/5より
α^5=cos2π+isin2π(ド･モアブルの定理より)
α^5=1･･･①
⇔α^5-1=0
⇔(α-1)(α^4+α^3+α^2+α+1)=0
⇔α^4+α^3+α^2+α+1=0･･･②(∵α≠1)
(1-α)(1-α^2)(1-α^3)(1-α^4)
={(1-α)(1-α^4)}{(1-α^2)(1-α^3)}
={2-(α+α^4)}{2-(α^2+α^3)}(∵①)
=4-2(α+α^2+α^3+α^4)+α^3+α^4+α^6+α^7
= 4-2(α+α^2+α^3+α^4)+α+α^2+α^3+α^4(∵①)
=4-(α+α^2+α^3+α^4)
=4-(-1)(∵②)
=5
