Homework Help Overview
The problem involves proving that (n-1) divides (n^k - 1) for integers n and k, where n is at least 2 and k is at least 2. Additionally, it seeks to establish that if (n^k - 1) is prime, then n must equal 2 and k must be prime.
Discussion Character
- Exploratory, Assumption checking
Approaches and Questions Raised
- The original poster considers using proof by induction as a potential approach but expresses uncertainty about how to proceed. Some participants provide a hint involving a factorization of (n^k - 1), while others clarify the notation used in the problem statement.
Discussion Status
The discussion is ongoing, with participants exploring different interpretations of the problem and clarifying the expression involved. A hint has been provided, but there is no explicit consensus or resolution yet.
Contextual Notes
There is a focus on the correct interpretation of the expression (n^k - 1), with some participants questioning the notation used in the original post.