Question

what is remainder when 13^400 is divided by 187?

Answer 1

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Answer 2

Given:

13^400 is divided by 187.

To Find:

The remainder when 13^400 is divided by 187.

Solution:

13^400 / 187.

187 = 11*17.

Divide separately,

13^400 / 11.

Euler of 11 is 10,

So,

a^10 / 11.

1 is the remainder.

So,

13^400 / 11.

= (13^10)^8 / 11.

= 1^8 / 11.

= 1 / 11.

1 is the remainder.

Now,

13^400 / 17.

Euler of 17 is 16.

a^16 / 17.

1 is the remainder.

13^400/17.

= (13^16)^13/17.

= 1^13/17.

= 1/17.

1 is the remainder.

From both we got the remainder 1.

Hence, the remainder when 13^400 is divided by 187 is 1.