(51)^61 what will remainder if divided by 7?
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51^61 /7 can be written as
(49 +2)^61/7
For any power, 49 is divided by 7. SO, required remainder will depend on
2^61/7 ==Remainder == 2^(4*15 +1)/7, it will be same as
2^1/7, So,
Required Remainder = 2.