$n = \sum_i d_i = \sum_i d_i^{-1} \implies d_i = 1$
Hint
$$ \sum_{i=1}^n d_i = \sum_{i=1}^n d_i^{-1}= n\implies \sum_{i=1}^n d_i+d_i^{-1}= 2n $$ Now simply use $$x+\frac{1}{x}\ge 2\quad,\quad x>0.$$
$n = \sum_i d_i = \sum_i d_i^{-1} \implies d_i = 1$
Hint
$$ \sum_{i=1}^n d_i = \sum_{i=1}^n d_i^{-1}= n\implies \sum_{i=1}^n d_i+d_i^{-1}= 2n $$ Now simply use $$x+\frac{1}{x}\ge 2\quad,\quad x>0.$$