RTP: If , then , where a,b are positive integers
Proof
Note
Assume
Then
Thus
So
So
This is impossible, so our assumption is wrong
Thus our statement is true
Questions
1. Is this proof valid?
2. Can I generalize to :If gcd(a,b)=k, then gcd(a, (a+b))=k
3. Is there a simpler non-contradiction, non-FTA proof?