Question

n
x^n+1-x^n-x+1 is exactly divisible by (x-1)^2if n is
n​

Answer 1

Answer:

n+1

+(x+1)

2n−1

=x

2

+(x+1)=x

2

+x+1, which is divisible by x

2

+x+1.

For n=2, we have

x

n+1

+(x+1)

2n−1

=x

3

+(x+1)

3

=(2x+1)(x

2

+x+1), which is divisible by x

2

+x+1.

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