TR-MO 2007 Problem 4

Let $k>1$ be an integer, $p=6k+1$ be a prime number and $m=2^{p}-1$ .

Prove that $\frac{2^{m-1}-1}{127m}$ is an 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.