# Uproot this recurrence

Algebra Level 5

Let $${a_n}$$ be the sequence of real numbers defined by $$a_1 = t$$ and $$a_{n+1} = 4a_n(1 - a_n)$$ for $$n \geq 1$$.

If the number of distinct values of $$t$$ such that $$a_{1998} = 0$$ is $$x$$, find the value of $$x \pmod {1000}$$.

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