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Is it true that :

If $a^n+n^{a}$ is prime number and $a=3k-1$ then $n\equiv 0\pmod 3$

where $a>1,n>1 ; a,n,k \in \mathbb{Z^+}$

I have checked statement for many pairs $(a,n)$ and it seems to be true.

Small Maple code that prints $(a,n)$ pairs :

enter image description here

Any idea how to prove this statement ?

2 Answers 2