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I have three positive integers, a, b, and c. I know that $a\oplus b\oplus c=0$, so I got that each pairwise xor has to be the other positive integer. $a\oplus b=c$, $b\oplus c=a$, and so on, but I can't find a, b, and c.

There are lots of solutions, (I'm pretty sure), I'm just trying to code a quick way to find all of the solutions

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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

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    $\begingroup$ As explained, the set of solutions is 2-dimensional in that 3-dimensional space--it's a big "infinitely many". $\endgroup$
    – Zachary Vance
    Commented Nov 7, 2020 at 7:12

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