Number theory prime divisibility problem

Hello, as part of a proof I am working on, I need to find all s.t. and . and is prime. This part of my proof has stumped me and I have had no success in attacking this part and I am not sure as to whether I am just going down a blind alley here and there is more efficient way. Any help/ ideas/ hints would be much appreciated.

Re: Number theory prime divisibility problem

Finding all such is not a proof. Proving that the set of all such you find is a proof. What do you have so far?

Re: Number theory prime divisibility problem

Quote:

Originally Posted by

**SlipEternal** Finding all such

is not a proof. Proving that the set of all such

you find is a proof. What do you have so far?

Thank you for taking the time to reply. :)

My apologies as it was poor wording in the post 1. This is not the question itself that I am working on but is the route I have taken down towards my solution of another question. Essentially, I am trying to prove that (or what I was trying to convey in the first post was that I was ultimately trying to show the only such that exists is 2 - I do not know this to be true or not, I have only conjectured) and I haven't been able to make any progress in this part of the solution so I was inquiring whether this is even true to begin with (i.e. if anyone could think of a counterexample) and even if it is true, is the proof of it tangible (and if anyone could give me a hint as to how to start to prove this).

Re: Number theory prime divisibility problem

Quote:

Originally Posted by

**SlipEternal** Finding all such

is not a proof. Proving that the set of all such

you find is a proof. What do you have so far?

Actually, nevermind, the conjecture is incorrect, I have found a counterexample. Back to the drawing board, I suppose..

Re: Number theory prime divisibility problem

Re: Number theory prime divisibility problem

^embarrassingly i have found yet another hole in my above argument in post #5. :( even can very well be a solution