Let me explain to you how a "assume-contradiction" proof work like. If assume something is true, then using a series of conclusion you arrive at a statement which is contradictory. But you need to explain how you arrived at your contradictory statement.Originally Posted by OReilly
Follow the link of logical statements.
1)We have this statement.
2)We deduce this one.
3)This one is just expressed in mathematical terms.
4)Because if with then .
5)Because a prime divides a square (explained before).
Note, from steps 1 though 5 each one was a deduction on the one before. IF YOU CAN deduce step six from the previous 5 then you reach step 6 which is a contradiction. Which means your initial hypothesis (your original problem) was false. But to do that you need to demonstrate how step six is related to the other five. You failed to do that. You used wrong theorems on divisibility. However if you CAN provide a logical deduction on step 6 then you arrive at a contradiction and you complete your proof.
Here is an example of what you are doing.
I am going to prove there are infinitely many primes.
1)Assume there are finitely many primes.
4)Thus there must be infinitely many primes.
Note, Step 2 CANNOT BE DEDUCED from step 1 thus it was a faulty prove. You are doing the same, you are faulty believing that you can deduce step 6 from step 5 which is false there is not such theorem on divisibility.
In basic terms your proof is wrong.