# Can we find three odd numbers satisfying this relation? [closed]

If $a^2+b^2=c^2$ and $(a, b, c) \in \mathbb N^3$ are natural numbers. Can we find three odd numbers satisfying this relation?

• Where do you see a pair when $a,b,c$ are three numbers? – Hagen von Eitzen Jul 17 '16 at 9:08
• How can two odd numbers add up to another odd number – Archis Welankar Jul 17 '16 at 9:09
• That is the question actually.. It is either possible or not possible.. I am asking for if it is possible – danny Jul 17 '16 at 9:12
• The title says one thing, the body says another. – barak manos Jul 17 '16 at 9:38

The square of an odd number is still odd, and the square of an even number is even. So a number $x$ is odd if and only if its square $x^2$ is odd.
We deduce $a^2 + b^2$ is even, so $c^2$ is even, and $c$ is even. Contradiction.
Let $a, b$ be odd. Then $a^2, b^2$ are as well. Thus, $a^2 + b^2$ is even, which means that $c^2$ is even. Thus, $c$ cannot be odd with $a, b$ even.