Thanks for your proposed solution to 2007 IMO Problems/Problem 5. Unfortunately, there's a flaw with it, so I've commented out your solution for now, but it's easy to replace if you can fix it.
Note that may not be prime (in fact, if the problem statement holds, then it's almost certainly not prime, as it factors as a difference of squares). So in general, does not imply that or . This is bad, because you appear to use this implication in your solution when you move from to . It is okay to say that , since is pretty clearly relatively prime to , but we need some more argument here. In particular, we could (hypothetically) have and or something like that. It could be the beginning of a nice solution, though.
Boy Soprano II 03:02, 23 November 2009 (UTC)