Show that the power series $$\sum_{m=0}^{\infty} x^{m^2} = \sum_{n=0}^{\infty} c_n x^n$$ where $c_n = 1$ if $n$ is the square of an integer $m \geq 0$ and $c_n = 0$ otherwise, is not the power series expansion of a rational function.
Show that the power series
$$\sum_{m=0}^{\infty} x^{m^2} = \sum_{n=0}^{\infty} c_n x^n$$
where $c_n = 1$ if $n$ is the square of an integer $m \geq 0$ and $c_n = 0$ otherwise, is not the power series expansion of a rational function.