Question 146
Do there exist pairwise distinct natural numbers $a_1, a_2, \dots, a_k$, greater than $1$, for which
$$
a_1 + a_2 + \dots + a_k = 2010 \cdot \left( \frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_k} \right)
$$
a) if $k=2$;
b) if $k=12$.
$$
a_1 + a_2 + \dots + a_k = 2010 \cdot \left( \frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_k} \right)
$$
a) if $k=2$;
b) if $k=12$.