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Algebra

Cool goIITian

 Joined: 13 Jan 2011 Post: 54
19 Jan 2011 14:13:44 IST
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1810
What will be remainder when 2^2007 is divided by 17?
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What will be remainder when 2^2007 is divided by 17?

Hot goIITian

Joined: 6 Aug 2010
Posts: 194
19 Jan 2011 14:43:13 IST
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2^2007 = (2)^7 *(2^4)^500 = 128(17-1)^500 = 128(17@+1), where @ ? I, therefore, Remainder = 128.

Hot goIITian

Joined: 6 Aug 2010
Posts: 194
19 Jan 2011 14:44:18 IST
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Above, @ is an element of I.

Cool goIITian

Joined: 13 Jan 2011
Posts: 54
19 Jan 2011 15:08:10 IST
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thanx

Forum Expert
Joined: 28 Feb 2007
Posts: 2217
20 Jan 2011 12:29:28 IST
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Since when did we abandon the convention that the remainder is to be less than the divisor?

Cool goIITian

Joined: 13 Jan 2011
Posts: 54
20 Jan 2011 14:19:21 IST
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yo! u r rght..... I thanked him for method......

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
20 Jan 2011 14:28:46 IST
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Cool goIITian

Joined: 13 Jan 2011
Posts: 54
20 Jan 2011 14:39:02 IST
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As we have got 128(17-1)^500. We can see (17-1)^500 is a binomial expansion in which all term will contain a multiple of 17 except first term which is (17^0)*(-1)^500 which equals 1 now 128 is multiplied and this is the only term which is not divisible by 17 and we can get the remainder by dividing 128 by 17 which is also the remainder for 2^2007.

New kid on the Block

Joined: 18 May 2013
Posts: 2
18 May 2013 10:53:46 IST
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i think the answer shoul be 92^2007/17=(2^4)^501 * 2^3/17=16^501 * 8/17=(-1) * 8/17 using the negetive remainder=-8=17-8=9ans//

New kid on the Block

Joined: 18 May 2013
Posts: 2
18 May 2013 10:54:40 IST
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i think the answer should be 9.......because2^2007/17=(2^4)^501 * 2^3/17=16^501 * 8/17=(-1) * 8/17 using the negetive remainder=-8=17-8=9ans//

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