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Problem Solving (PS) | Re: What is the remainder when 2^86 is divided by 9?

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jabhatta@umail.iu.edu wrote:

Bunuel ,VeritasKarishma

Just wondering -- how to use the binomial method for the following

source : made up

(2^10)/9


\( 2^{10} = 2 * 2^9 = 2 *8^3\)

\( = 2 * (9 -1)^3\)

The remainder term when (9 - 1)^3 is divided by 9 is -1 and since all terms are multiplied by 2, the remainder is -2.
This is the same as remainder of 7.
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