XOR of three integers where each pair's XOR is the other integer
There are infinitely many solutions: choose $a=b\in\mathbb N, c=0$ and then $a\oplus b\oplus c=0$.

To find all solutions, choose an arbitrary $c\in\mathbb N$. We want to find all $a,b$ with $a\oplus b=c$. Its equivalent to $a=b\oplus c$, so for every $b\in\mathbb N$ we would choose $a=b\oplus c$ and $a,b,c$ would be a valid solution. 

All of the solutions are of this form - and therefore thats how you can iterate through every possible solution to the question