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Does $\sum_{n \geq 0} a_n x^n=\sum_{n \geq 0} b_nx^n$ imply $a_n=b_n$ for vector-tuple power series?
My reference is Infinite series in p-adic fields by Keith Conrad.
Corollary 5.6. If $f(x)=\sum_{n≥0} a_nx^n$ has a positive radius of convergence in the $p$-adic field $\mathbb Q_p$ then $f$ is ...
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