Problem: The only consecutive non-negative integers a,b and c that satisfy $a^2+b^2=c^2$ are $3,4$ and $5$.
Firstly, How can i turn this into logical statement?
Let $a,b$ and $c$ are consecutive
- $a \in \mathbb N, a^2+b^2=c^2 \implies a = 3 $
- $a \in \mathbb N, a = 3 \implies a^2+b^2=c^2$
I think first one is true, but i have a little confusion..
Then how can i prove it by contradiction?
we know $[(P'\implies q ) \land q' ] \implies P$
we want to show that $a^2+b^2 \ne c^2 \implies a=3 $ is wrong
$a^2 - 2a - 3 = (a-3)\cdot(a+1) \ne 0 \implies a\ne 3$
This completes proof, right?