what is the remainder when 128^500 is divided by 153?

understood till

Euler number of 153 is 96 so the number reduces to 128^20

153 = 17 * 9

Now he says..
17 leaves a remainder of 16 and 9 leaves a remainder of 4
17A+16= 9B + 4

i did not get the above two steps! :) Help Please!

Question

what is the remainder when 128^500 is divided by 153?

understood till

Euler number of 153 is 96 so the number reduces to 128^20

153 = 17 * 9

Now he says.. 
17 leaves a remainder of 16 and 9 leaves a remainder of 4
17A+16= 9B + 4

i did not get the above two steps! :) Help Please!

anonymous · Answer

if you can explain how these statements work, then I would have an idea on the approach ! 

(36^41) mod 7 = 1  ?? how
(36^41) mod 11 = 3 ?? how

anonymous · Answer

@mukushla

anonymous · Answer

ur problem is with this 2 steps :

$$36^{41} \mod 7 = 1$$$$36^{41} \mod 11 = 3$$ 
?