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remainder when 22^56 is divide d by 7?22^56 means 22 to the power 56??

remainder when 22^56 is divide d by 7?22^56 means 22 to the power 56??

Grade:10

1 Answers

Fawz Naim
37 Points
10 years ago

This question can easily be solved by using binomial theorem.

22^56 can be written as (21+1)^56. Now applying binomial theorem

56C0 21^56+56C1 21^55+56C2 21^54+...........+56C56 21^0

=21(56C0 21^55+56C1 21^54+56C2 21^53+.............+56C56 21^-1)

let 56C0 21^55+56C1 21^54+56C2 21^53+..............+56C56 21^-1)=a

=21a   which is divisible by 7 so the remainder is zero

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