TITLE: Lattice points on a hyperbola.
QUESTION [0 upvotes]: A lattice point in the $xy$-plane is a point both of whose coordinates are integers (not necessarily positive). How many lattice points lie on the hyperbola $x^2-y^2=17$?
I think the answer should be $4$, because $x^2-y^2 = (x+y)(x-y) = 17$. $17$ has $4$ factors: $1, 17, -1,$ and $-17$. But I don't know if these numbers actually work.

REPLY [1 votes]: Yes, they work:
$x+y=17$ and $x-y=1\implies 2x=18\implies x=9\implies y=8$
$x+y=1$ and $x-y=17\implies 2x=18\implies x=9\implies y=-8$
$x+y=-17$ and $x-y=-1\implies 2x=-18\implies x=-9\implies y=-8$
$x+y=-1$ and $x-y=-17\implies 2x=-18\implies x=-9\implies y=8$
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