### Remainder theorem + Binomial

Posted:

**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

Your one-stop shop for all MBA information.

http://theindianmba.com/forums/

Page **1** of **1**

Posted: **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

Posted: **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.

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.