# Fibonacci and Square Numbers - The Court of Frederick II

Author(s):
In modern notation this means finding $$x,y,$$ and $$z$$ so that $$x^2 + 5 = y^2$$ and  $$x^2 - 5 = z^2.$$
This is easy enough if you allow irrational solutions, for instance taking $$x=\sqrt{17},$$ $$y=\sqrt{22},$$ and $$z=\sqrt{12}.$$ But further reading makes it clear that Leonardo is looking for a rational solution (it is not hard to see that a solution in integers is impossible). His work then leads him to consider many more questions about sums and differences of squares.