Find the remainder of 2^1000 when divided by 3?

2^1/3 = 2
2^2/3= 1
now wen 2^2 div by 3 gives d rem ,dis proves dat d cyclicity is 2...wen 1000 z completely div by 2 d rem is also 1...hence d answer z 1....

(3-1)^1000 = -1^1000 = -1 =>2