# Taking these type of problems to a new level

Algebra Level 4

Suppose that a real number $$x$$ satisfies the equation

$$x^2+\frac{1}{x^2}=3$$

Define a sequence $$a_{n}$$ as $$a_{n}=x^n+\frac{1}{x^n}$$. How many of $$a_{1}, a_{2}, \cdots a_{1000}$$ are integers?

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