Number Theory: $x^2+y^2=a^2$ Is there a coprime triple $(x,y,z)$ such that $x^2+y^2=a^2, x^2+z^2=b^2, y^2+z^2=c^2$, where $a,b,c$ are integers

P.S. such solution doesn't exist for $a,b,c&lt;1000$, as the computer says

P.P.S. the statement above is WRONG
It's called Euler brick,the smallest one is $x=44,y=117,z=240$

http://en.wikipedia.org/wiki/Euler_brick
x = 720
y = 132
z = 85
a = 732
b = 725
c = 157