# This Question Should Have Been Posted 3 Years Ago

**Number Theory**Level 4

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.