The question: Every expression of the form $a^2b^2 + b^2c^2 + c^2d^2 + d^2a^2$ can be expressed as the sum of two squares in at least two different ways. Find any one of the three possible ordered pairs of positive integers $(x, y)$, with $x > y$, that satisfies $x^2 + y^2 = 44^2 \cdot 10^2 + 10^2 \cdot 33^2 + 33^2 \cdot 5^2 + 5^2 \cdot 44^2$.
What I found: From factorizing, we see that the first expression is just $(a^2 + c^2)(b^2 + d^2)$. $1 = (0 + 1)(0 + 1)$ and $2 = (0 + 1)(1 + 1)$ are of this form, but they cannot be expressed two different ways. Also, if $2$ is the sum of two squares, then it's also implied that $4 = 2 \cdot 2$, $8 = 4 \cdot 2$, and generally all powers of two should be expressible as a sum of two squares two different ways, but $8$ is another counterexample.
Am I misinterpreting the question, or is it wrong? Also, how do I actually tackle finding $x$ and $y$ for the last sentence of the question?