CIIM 2011 Problem 2

Let $k$ be a positive integer, and let $a$ be an integer such that $a-2$ is a multiple of $7$ and $a^6-1$ is a multiple of $7^k$ .

Prove that $(a + 1)^6-1$ is also a multiple of $7^k$ .

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.