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If 5^(99) is divided by 13, the remain...

If ` 5^(99) ` is divided by 13, the remainder is

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
d
Let ` P = 5^(99) = 5xx5^(98) = 5(25)^(49) = 5(26-1)^(49)`
`= 5[""^(49)C_(0) (26)^(49) - ""^(49)C_(1) (26)^(48) + ""^(49)C_(2)(26)^(47) - ...+ ""^(49)C_(48) (26) - ""^(49)C_(49)*]`
` = 5xx26k - 5`, when k is an interger.
` therefore (P)/(13) = 10k - (5)/(13) = 10k -1+ (8)/(13)`
Hence , the remainder is 8.
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