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 \(x²-y²=17\)?

Guest Aug 19, 2019

#1**+1 **

A lattice point in the -plane is a point both of whose coordinates are integers (not necessarily positive). How many lattice points lie on the hyperbola ? \(x^2-y^2=17\)

\(x^2-y^2=17\\ y=\pm\sqrt{x^2-17}\)

\(x\in \mathbb Z\ |\ \{[x^2-17]\}\subset \{squares\}\)

There are only four grid points P.

\(P_1(-9,-8)\\ P_2(-9,\ 8)\\ P_3(9,-8)\\ P_4(9,\ 8)\\\)

!

asinus Aug 19, 2019