Determine all positive integers $n$ for which the equation \[x^{n}+(2+x)^{n}+(2-x)^{n}= 0\] has an integer as a solution.
Source:
Tags: Diophantine Equations
Determine all positive integers $n$ for which the equation \[x^{n}+(2+x)^{n}+(2-x)^{n}= 0\] has an integer as a solution.