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(1) Show that if there is one lattice point (point with integer coordinates) on the parabola $$y=ax^2$$ then there are infinitely many.
(2) Find all the lattice points on the hyperbola $$x^2 - y^2 = 84.$$
Lattice Points
Age 16 to 18
Challenge Level 
(1) Show that if there is one lattice point (point with integer coordinates) on the parabola $$y=ax^2$$ then there are infinitely many.
(2) Find all the lattice points on the hyperbola $$x^2 - y^2 = 84.$$
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