# This Question Should Have Been Posted 3 Years Ago

Let $$j= \dbinom{2011}{0} 3^0 + \dbinom{2011}{1} 3^1 + \dbinom{2011}{2} 3^2 + \cdots + \dbinom{2011}{1005} 3^{1005}.$$ Find the remainder when $$2^{2011}-j$$ is divided by $$2011^2.$$

Details and assumptions

• This problem is not original.

• You might use the fact that $$2011$$ is prime.

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