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# What is the remainder when 11^704 is divided by 17 ?

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Re: What is the remainder when 11^704 is divided by 17 ? [#permalink]
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11^704 divided by 17
11^2 = 121 which when divided by 17 gives 2 as remainder
2^(704/2) = 2^352. Now 2^4 = 16 and 16/17 = -1
so we can write as
(-1)^(352/4) = (-1)^88 = 1
Therefore, the remainder is 1
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Re: What is the remainder when 11^704 is divided by 17 ? [#permalink]
sivakumarm786 wrote:
11^704 divided by 17
11^2 = 121 which when divided by 17 gives 2 as remainder
2^(704/2) = 2^352. Now 2^4 = 16 and 16/17 = -1
so we can write as
(-1)^(352/4) = (-1)^88 = 1
Therefore, the remainder is 1

Could you please explain the last part where 16/17=-1 ???
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Re: What is the remainder when 11^704 is divided by 17 ? [#permalink]
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suddu wrote:
sivakumarm786 wrote:
11^704 divided by 17
11^2 = 121 which when divided by 17 gives 2 as remainder
2^(704/2) = 2^352. Now 2^4 = 16 and 16/17 = -1
so we can write as
(-1)^(352/4) = (-1)^88 = 1
Therefore, the remainder is 1

Could you please explain the last part where 16/17=-1 ???

Hi suddu

this is negative remainder. In the ibid case, 16/17 gives 16 as remainder or it can be seen as -1 (-1 + 17 = 16) as well.

Best Wishes
Siva kumar
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Re: What is the remainder when 11^704 is divided by 17 ? [#permalink]
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Re: What is the remainder when 11^704 is divided by 17 ? [#permalink]
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