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 $r_1+r_2$ .

a^x

a-1

a+1

ax

ax+1

a