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I have been going at this question for weeks now and couldn't find anything.
Can we have a series of the form:
$$f(x)=\sum_{n=0}^{\infty} a_n x^n$$
where $a_n$ are rationals and not all $0$ such that $f(e)=0$?
Just like how $\pi$ is a root of the power series of $\sin(x)$ function:
$$\sin(x) = \s...