MathNet 2021 — Part 09 Question 71

Question 71

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 $y - 1 = x$
$x + y + z = 1$