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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.

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

!

Aug 19, 2019
edited by asinus  Aug 19, 2019
#2
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All right, thanks!

Guest Aug 19, 2019