# Power Trap

A sequence of pairs of integers $$(x_0,y_0),\ (x_1,y_1),\ (x_2,y_2),...$$ is defined, starting from some initial pair $$(x_0,y_0),$$ by the following formulas: $\begin{cases} x_{k+1}=x_k^4y_k-x_k^3y_k^2\\ y_{k+1}=x_k^2y_k^3-x_ky_k^4 \end{cases}$ Find the number of primes $$p<1000$$ such that $$x_{10}$$ is a multiple of $$p$$ for all initial pairs $$(x_0,y_0)$$.

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