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Avishek
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Post subject: Remainder theorem + Binomial  Posted: Fri Jun 25, 2010 3:43 pm |
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(111^11)/(11^11) will give a remainder of? I know that Binomial can be used but can't figure out how
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Amey
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Post subject: Re: Remainder theorem + Binomial Posted: Mon Jun 28, 2010 9:37 pm |
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111^11 can be written as (110+1)^11
If you expand the binomial, it is -
110^11 +
(11C1)110^10 +
(11C2)110^9 +
... +
1
Observe that each of the terms - 11C1, 11C2.. 11C10 are divisible by 11, as 11 is a prime number. So, the remainder is 1.
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