Q.

When 599 is divided by 13, the remainder is

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a

8

b

9

c

10

d

none of these

answer is A.

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Detailed Solution

We have, 599=53⋅596=(125)(625)24 =[13×9+8](1+48×13)24 =(13×9+8)[1+24C1×(48×13)+24C2(48×13)2+…+(48×13)24]= 8 + terms containing powers of 13. Hence remainder = 8.
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When 599 is divided by 13, the remainder is