Also C-B>1
It seems you are desperately trying to create a new conjecture. Well after putting 10489 new constraints into the original one, since it still doesn't work i think you should start from scratch to create a valid conjecture.
The counterexample of the new constraints:
P=5
Q=2
n=3
K1=1426
C=35
B=2
ChessTal has speedily assisted me so far and the counterexamples he found were very useful because the gaps in the conjecture have been closed. Of course I can spend time learning a computer program and writing one to search for counterexamples but I don't think any will be found when all the constraints are imposed. If any is found then I will give up on the conjecture.
Whereas ChessTal seems to be very happy to help you out you have apparently made little or no effort in the solution process. Repay that willingness by making a stab at it yourself. Your stab may not work. Post it anyway and maybe we can teach you where your mistake is and to learn how to do it yourself. That is, after all, the whole point of the learning process.
We are a help site. We do not exist to solve all your problems.
-Dan
I think the conjecture is a theorem given all the constraints. ChessTal was using particular values for the variables to get counterexamples. This made me come up with more and more constraints and I've checked that there can be no more constraints. We were getting somewhere yesterday because he seemed surprised his computer was taking 2 minutes to come up with a counterexample and he said he needed to look for counterexamples using a different method today. I am patiently waiting and hoping he would say he didn't find any. If he does then I would then move on to proving the conjecture with suggestions from members of the forum. My proof is simply based on the fact that all C^n - B^n factorise in one and only one way and therefore anything different from this way, given all the constraints cannot be a C^n - B^n.