# $3$ primitive pythagorean triples from 6 integers.

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

• Apologies for the confusion caused by my initial post (I really did try to not make a mistake, sigh), I've now edited it. – fuzzy Jan 26 '18 at 11:05
• 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. – Arthur Jan 26 '18 at 12:38