Show that for any sequence $a_1,a_2,...$ of real numbers, the two conditions
$\lim_{n\to\infty}\frac{\exp(ia_1)+\exp(ia_2)+...+\exp(ia_n)}{n}=\alpha$
and
$\lim_{n\to\infty}\frac{\exp(ia_1)+\exp(ia_4)+...+\exp(ia_{n^2})}{n^2}=\alpha$
are equivalent.