n e N, and n = 5 (mod6). prove that n^2 + 2 is composite. Can someone give me a detailed, step by step proof of how to do this?? I'm completely confused when it comes to modular arithmetic
n e N, and n = 5 (mod6). prove that n^2 + 2 is composite. Can someone give me a detailed, step by step proof of how to do this?? I'm completely confused when it comes to modular arithmetic
Hence
So
It should be obvious that 3 divides . And since , it follows that , and hence .
It might be worth mentioning also that for all It’s clear in this particular problem, but this is something which people tend to neglect when doing this sort of problems.
Last edited by TheAbstractionist; May 16th 2009 at 02:30 PM.