AUSTRIAN-POLISH 1979 Problem 9

Find the greatest power of $2$ that divides $a_n = [(3+\sqrt{11} )^{2n+1}]$ , where $n$ is a given positive integer.

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.