# There is no function $f$ on the open unit disk, defined by a convergent power series, such that $f(1/n)=(-1)^n/n^2$

Prove that there is no function $f$ on the open unit disk, defined by a convergent power series, such that $f(1/n)=(-1)^n/n^2$.

I'm not sure how to start... any hints would be appreciated!

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Hint: Let $g(z) = z^2$ and look at points where $f(z) = g(z)$.