If `2^33` is divided by `17`, then the remainder is
(1)    `15`        (2)    `2`        
(3)    `4`        (4)    `9`

Explanation

`17` can be written as `2^4+1`. So, we have to create factors of `2^4+1` to solve this question.

`2^33 = 2^33-2^9+2^9-2+2`

` = 2^9(2^24-1)+2(2^8-1)+2`

As, `a^2 - 1 = (a+1) (a-1)`, we can write our expression as,

` = 2^9(2^12-1)(2^12+1)+2(2^4-1)(2^4+1)+2`

` = 2^9(2^12-1)((2^4)^3+(1)^3)+2(2^4-1)(2^4+1)+2`

As, `a^3 + 1 = (a+1) (a2-a+1)`, we can write our expression as,

` 2^33= 2^9(2^12-1)(2^4+1)(2^8-2^4+1)(2^4-1)(2^4+1)+2`

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