show that the area of any pythagorean triangle is integer

Question

rational · Answer

A triangle with integer sides is called pythagorean triangle

dan815 · Answer

gotta show one one of the sides is divisible by 2

rational · Answer

i have a proof which i don't like much... so im really looking for alternatives here

rational · Answer

yes i think that will do !

kainui · Answer

We have to show that if a and b are odd that there is no way c can be an integer I think.

dan815 · Answer

we know that one of the sides is definately
and

odd^2 + odd^2 = something^2

dan815 · Answer

oh kai

rational · Answer

nice ideas 


odd + odd = even 

why is this harmful

kainui · Answer

$$\Large A=\frac{ab}{2}$$ if they're both odd then the area isn't an integer.

rational · Answer

yes thats another way to state the problem, not a solution/proof.

kainui · Answer

Right, that's just my reasoning for why it's important though.

rational · Answer

I see so it is sufficient to show that one of legs is even

kainui · Answer

No, what I'm saying is there is no integer c we can choose to make this statement true $$\Large (2n+1)^2+(2m+1)^2 = c^2$$

dan815 · Answer

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