MathNet 2021 — Part 09 Question 91

Question 91

Which of the following conditions is sufficient to guarantee that integers $x$, $y$, and $z$ satisfy the equation
$$
x(x - y) + y(y - z) + z(z - x) = 1?
$$

$x\gt y$ and $y=z$
$x=y-1$ and $y=z-1$
$x=z+1$ and $y=x+1$
$x=z$ and $y-1=x$
$x+y+z=1$