Question 75
Find all pairs of positive integers $(n, k)$ such that all sufficiently large odd positive integers $m$ are representable as
$$
m = a_1^{n^2} + a_2^{(n+1)^2} + \dots + a_k^{(n+k-1)^2} + a_{k+1}^{(n+k)^2}
$$
for some non-negative integers $a_1, a_2, \dots, a_{k+1}$.
$$
m = a_1^{n^2} + a_2^{(n+1)^2} + \dots + a_k^{(n+k-1)^2} + a_{k+1}^{(n+k)^2}
$$
for some non-negative integers $a_1, a_2, \dots, a_{k+1}$.