Anik's remainders

Anik likes division and is always eager to find remainders.

Once Anik divided $$a^x$$ by $$(a-1)$$ to get positive remainder $$r_1$$; and by $$(a+1)$$ to get positive remainder $$r_2$$.

If Anik assumed $$a$$ as a positive integer greater than 2 and $$x$$ as an positive odd number greater than 1, find $$r_1+r_2$$.

I made this problem as a simple generalization of this problem.
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