# A lattice point in the xy-plane is a point both of whose coordinates are integers (not necessarily p

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 ${x}^{2}-{y}^{2}=\left(x+y\right)\left(x-y\right)=17$. 17 has 4 factors: 1,17, -1, and -17. But I don't know if these numbers actually work.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

jaewonlee0217fyv
Step 1
$x+y=17$ and $x-y=1⇒2x=18⇒x=9⇒y=8$
$x+y=1$ and $x-y=17⇒2x=18⇒x=9⇒y=-8$
Step 2
$x+y=-17$ and $x-y=-1⇒2x=-18⇒x=-9⇒y=-8$
$x+y=-1$ and $x-y=-17⇒2x=-18⇒x=-9⇒y=8$.