TR-MO 2003 Problem 4

Suppose that $2^{2n+1}+ 2^{n}+1=x^{k}$ , where $k\geq2$ and $n$ are positive integers. Find all possible values of $n$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.