Integer solutions on summation of primes powers

Question

Let $\alpha$ be any prime number and $n_1\ge n_2\ge n_3$, $k_1\ge k_2\ge k_3$. If $\alpha^{n_1}+\alpha^{n_3}+\alpha^{n_3}=\alpha^{k_1}+\alpha^{k_2}+\alpha^{k_3},$ does this implies $n_1=k_1,n_2=k_2,n_3=k_3$?

Answer 1

Counter-example:

$2^3+2^3+2^3=2^4+2^2+2^2$