Originally Posted by
berachia If you assume n=3k then case closed
n=3k+1 then n+2=3(k+1)
n=3k+2 then n+4=3(k+2)
So, that proves it?
How would you formally write this assuming nothing excepting basic axioms or addition etc.
Are there any other proofs?
Is there any way of obtaining every single proof of a question like this in general? Suppose you found 10 proofs out of 10, how would you prove or ascertain that there is no eleventh proof? Or is this idiotic speculation?
If you add the three you get 3(n+2), is it true that the sum of 3 different integers, if divisible by three, then at least one of the three must also be divisible by three? How is this proved, if so?