Algebra Level 3

Let $$P_n (x)$$ be a polynomial such that $$P_n (x) = P_{n-1} (x-n)$$.

Given that $$P_0 (x)= x^{90} - x^{89} + x^{88} - x^{87} + \cdots + 1$$, and $$P_{10} (x) = P_0 (x-k)$$, find $$k$$.

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