由 lskuo 於 星期四 十二月 05, 2013 10:32 am154 寫到:x^50+1除以(x-1)^2的餘式是多少?
Let x^50 + 1 = Q(x) (x-1)^2 + a(x-1) + b
When x = 1,
2 = b
Rewrite the equation as
x^50 + 1 - b = x^50-1= (x-1)[ Q(x)(x-1) + a]
Recall that
x^n -1 = (x-1)[1 + x + x^2 + ... + x^(n-1) ]
So
1 + x + x^2 + ... + x^49 = Q(x)(x-1) + a
When x = 1
50 = a
Ans = a(x-1) + b = 50x - 48