(When I use an $=$, I am referring to a congruence relation.)
I am curious is anybody can point me in the right direction for solving the following congruence relation ($a$,$b$ of course both integers)
$$a^b=b^a \mod (a+b)$$
I have tried rewriting this in a few forms, such as let $b=a+n$ and finding more likely scenarios for this to occur. However, I dont even know really how to approach writing a solution!
If anybody can just point me in the right direction, if I'm looking for abstract algebra terms, or some other form of math all together, that's all I really need!
Although, if you do have a solution, I would love to see that as well!