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Question

What will be the unit digit of (87)756355?

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Solution

Let (87)756355=(87)x where x=(75)6355=(75)odd
Cyclicity of 7 is 4,
To find the last digit we have to find the remainder when x is divided by 4.
x=(75)oddpower=(761)oddpower
where, x is divided by 4 so, remainder will be 1 or 3 but remainder should be positive always.
Therefore, the last digit is of (87)756355 will be 73=343.
Hence, the last digit is of (87)756355 is 3.

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