# Set theory or Number theory?

Number Theory Level 3

Let $$f(x) = x^2-a$$ and $$g(x) =x^2+b$$, where $$a$$ and $$b$$ are non-negative integers. What is the minimum value of $$a+b$$ such that $$f(\mathbb{Z} )\cap g(\mathbb{Z}) = \emptyset$$?

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