Remainder theorem + Binomial

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Remainder theorem + Binomial

Postby Avishek » Fri Jun 25, 2010 3:43 pm

(111^11)/(11^11) will give a remainder of? I know that Binomial can be used but can't figure out how

Re: Remainder theorem + Binomial

Postby Amey » Mon Jun 28, 2010 9:37 pm

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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