## Powerful Divisor

#### Problem

Consider the expression $x^x + 1$, where $x$ be a positive integer.

It can be verified that $x = 7$ is the least value for which $x^x + 1$ divides by $2^3$.

Given that $n$ is a positive integer, find the least value of $x$ for which $x^x + 1$ is divisible by $2^n$.

Problem ID: 319 (07 Apr 2007) Difficulty: 3 Star