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Find the remainder when 27^(40) is divid...

Find the remainder when `27^(40)` is divided by 12.

Text Solution

Verified by Experts

The correct Answer is:
18
`(7^(103))/(25) = (7(49)^(51))/(25)`
`= (7(50-1)^(51))/(25)`
`= (7(25k - 1))/(25)`
`= (175(k) - 25 + 25 -7)/(25)`
`= (25(7k - 1)+18)/(25)`
`= (25(7k-1)+18)/(25)`
Therefore, the remainder is 18.
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