Question 150
A certain country is taking part in the IMO this year for the 24th time. The team would like to mark the occasion by finding positive integers $n_1, \dots, n_{24}$ such that
$$
n_1^{24} + n_2^{24} + \dots + n_{24}^{24} = 2015^{2015}.
$$
Determine whether or not such a set of numbers exists.
$$
n_1^{24} + n_2^{24} + \dots + n_{24}^{24} = 2015^{2015}.
$$
Determine whether or not such a set of numbers exists.