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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 \(x²-y²=17\)?

 Aug 19, 2019
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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.

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

laugh  !

 Aug 19, 2019
edited by asinus  Aug 19, 2019
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All right, thanks! smiley

Guest Aug 19, 2019

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