Anik's remainders

Number Theory Level 3

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 \(r_1+r_2\).

Try more of my original problems in this set (click here).
I made this problem as a simple generalization of this problem.

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