1
$\begingroup$

Hi I was wondering about this and don't know how to solve it so thought I could ask about it here. If $A^2 + B^2 = X^2$ and $A^2 + C^2 = Y^2$ and $B^2 + C^2 = Z^2$ all are whole numbers and $A,B$ $A,C$ $B,C$ all form right angles in their respective triangles. Is there any solution or sets of numbers that fit. Regards Rob edit :- If there are many sets just the first few is fine.

$\endgroup$
1
$\begingroup$

Thanks I was just reading wiki before I saw your answer and this article https://en.wikipedia.org/wiki/Pythagorean_triple explains why my question can't be answered, one number needs to odd, and the other one even, so if both A,B and B,C are first part of a Pythagorean primitive triple, then B,C are either both even or both odd and can never make a Pythagorean triple.

$\endgroup$
  • $\begingroup$ You're correct that primitive Pythagorean triples consist of an odd and even "leg", but your question doesn't say that all three (or any) of the given relations have to be primitive. As André mentions, Wikipedia's "Euler Brick" entry explains that your question can be answered, and indeed that it has infinitely many solutions. $\endgroup$ – Blue Oct 3 '15 at 10:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.