Which of the following must be subtracted from 2^526 so that the resulting integer will be a multiple of 3?
Options
A) 1  B) 2  C) 3  D) 5  E) 6
2^12 is definitely NOT a multiple of 3 as 2^12 will only have 2s in it.   Coming back to the question,   2^1 leaves a remainder of 2 when divided by 3   2^2 leaves a remainder of 1 when divided by 3   2^3 leaves a remainder of 2 when divided by 3   2^4 leaves a remainder of 1 when divided by 3... etc. and the cyclicity continues.   Thus, 2^526 will leave a remainder of 1 when divided by 3. Thus you must subtract 1 from 2^526 to make it divisible by 3.   1 is thus the correct answer.
<result>A</result>
Which of the following must be subtracted from 2^526 so that the resulting integer will be a multiple of 3?