If n is a natural number, then 1-x-x^{n}+x^{n+1} is divisible by

Explanation

Factorizing the expression by grouping: 1 - x - x^n(1 - x) = (1-x)(1-x^n). Since n \geq 1, (1-x^n) can be expanded as (1-x)(1+x+\dots+x^{n-1}). Therefore, the entire expression contains (1-x)^2 as a factor.

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