What is the remainder obtained when $25^{68}$ is divided by 9?

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Solution

The correct option is C
5

$25^{68} = (18 + 7)^{68} = 27 k + (- 2)^{68} = 2^{66} + 2^{2} = 2^{[} 3^{22}] + 2^{2} = - 1^{22} + 2^{2}$
So the remainder obtained when $25^{68}$ is divided by 9 is 5.

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