KZ-MO 2002 Problem 7

Prove that for any integers $n> m> 0$ the number $2 ^n-1$ has a prime divisor not dividing $2 ^m-1$ .

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.