Question

Find the remainder of (29^31)^109/9​

Answer 1

Answer:

2 is the right answer.

Step-by-step explanation:

hope it helps you

Answer 2

Answer:

Remainder = 2

Step-by-step explanation:

Since

29 = 2 (mod 9)

By taking power 6 in both sides we get

29^6 = 2^6 (mod 9)

29^6 = 64 (mod 9) = 1 (mod 9)

since

31 * 109 =3379

And 6*563 = 3378

So taking the power of 563 on congruence we get

(29^6)^563 = (1)^563 (mod 9) = 1 (mod 9)

29^3378 = 1 (mod 9)

NOW multiplying by 29 on both sides we get

(29^3378)×26 = 1×29 (mod 9) = 29 (mod 9) = 2 (mod 9)

So

29^3379 = 2 (mod 9)

Thus

{(29^31)^109} = 2 (mod 9)

Thus

when we divide the (29^31)^109 by 9 we get remainder 2