Is there a way to solve this problem - sum of powers

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$N_1^a + N_2^a + \ldots + N_n^a$ Where a is any number.

Example $40^7+ 37^7 + 35^7 + 32^7 + ... 1^n=R$

If Iknow what $R$ is and that $ N_n$ is restricted to $0 \lt N_n \le 40$, Is there a way to find the $N_n$'s values used?