Show that the polynomial `x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3)` is divisible by `x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot`

Explanation

To show that the polynomial \( P(x) = x^{4p} + x^{4q+1} + x^{4r+2} + x^{4s+3} \) is divisible by \( Q(x) = x^3 + x^2 + x + 1 \), we need to verify that the roots of \( Q(x) \) satisfy \( P(x) \).

### Step 1: Identify the roots of \( Q(x) \)

The polynomial \( Q(x) = x^3 + x^2 + x + 1 \) can be factored as follows:

\[
Q(x) = \frac{x^4 - 1}{x - 1} \quad \text{for } x \neq 1
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