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$The remainder when 2^{2000} is divided by 17 is$

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− We have 24=16=17−1∴22000=24500=(17−1)500=500C017500−500C117499+500C217498−500C317497+…−500C499(17)+(−1)500= 17m+1, where m is some positive integer. required remainder is 1.

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The remainder when 22000 is divided by 17 is

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$The remainder when 2^{2000} is divided by 17 is$