1
$\begingroup$

Do there exist $3$ different primitive Pythagorean triples $(a,d,w), (a,b,z)$ and $(c,d,z)$?

Explicitly, we want $6$ different integers $a,b,c,d,w,z$ such that...

(1) $a^2 + d^2 = w^2$

(2) $a^2 + b^2 = c^2 + d^2 = z^2$

$\endgroup$
  • $\begingroup$ Apologies for the confusion caused by my initial post (I really did try to not make a mistake, sigh), I've now edited it. $\endgroup$ – fuzzy Jan 26 '18 at 11:05
  • 1
    $\begingroup$ I have written a piece of code that is currently looking, and it hasn't found any examples so far with $z\leq 350\,000$. Assuming the code is correct... It's still running, but it takes longer and longer to check. $\endgroup$ – Arthur Jan 26 '18 at 12:38
0
$\begingroup$

Unless I've made a mistake with my arithmetic these 6 will do...

a = 7015 b = 46248 c = 46535 d = 4752 w = 8473 z = 46777

$\endgroup$

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.