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Rearranging the equation, we have:

x^2 - 2xy + y^2 = 17

Factoring the left side of the equation, we get:

(x - y)^2 = 17

To find the lattice points, we need to find integer solutions for (x, y) that satisfy the equation.

Since 17 is a prime number, its only factors are 1 and 17. Therefore, the possible values for (x - y) are ±1 and ±17. Vampire Survivors

For (x - y) = ±1:

If (x - y) = 1, then we have the solution (x, y) = (1, 0).

If (x - y) = -1, then we have the solution (x, y) = (-1, 0).

For (x - y) = ±17:

If (x - y) = 17, then we have the solution (x, y) = (17, 0).

If (x - y) = -17, then we have the solution (x, y) = (-17, 0).

Therefore, there are four lattice points that lie on the graph of the given equation: (1, 0), (-1, 0), (17, 0), and (-17, 0).

mayomayo72218Aug 25, 2023