First up, I know there are a lot of similar questions with 24, not 12. So bare with me please :)
What is the Question?
Consider the following numbers of the form $p^2 - 1$ where $p$ is prime.
$$5^2 - 1 = 24$$ $$7^2 - 1 = 48$$ $$11^2 - 1 = 120$$
Each of these numbers is divisible by 12. Prove or provide a counter example to the following statement: "If $p > 3$ is prime, then $12 $ | $p^2 - 1$"
What have I tried?
Okay so off the cusp I know two methods that might help.
- Modular Arithmetic
- And that any prime $\geq$5 can be represented as $6k \pm 1 $
I'm only just catching up on course content and modular arithmetic so I don't really know where to start.
I assume because 12 | 24, the proof will be very similar to the ones provided on this forum for that question For any prime $p > 3$, why is $p^2-1$ always divisible by 24? I guess I wan't to make sure.