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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

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.

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