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Find the value of {3^(2003)//28}, w h e ...

Find the value of `{3^(2003)//28}, w h e r e{dot}` denotes the fractional part.

A

`17//28`

B

19/28

C

23/28

D

`2//28`

Text Solution

Verified by Experts

The correct Answer is:
b
Now , `(3^(2003))/(28) = (3^(2) xx3^(2001))/(28) = (9)/(28) (3^(3))^(667)= (9)/(28) (28-1)^(667)`
` = (9)/(28) {(28)^(667) - ""^(667)C_(1) (28)^(666)+ ""^(667)C_(2) (28)^(665) - ...+ ""^(667)C_(666) (28)-1}`
`= 9k - (9)/(28)` , where k is an integer .
` = (9k -1) + (19)/(98)`
or `{(3^(100))/(28)} = {(9k-1)+ (19)/(28)}= (19)/(28)`
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