How many lattice points are on the graph y=(x√2) -1?

Question

How many lattice points are on the graph y=(x√2) -1?
A lattice point is a point whose coordinates are both integers

Answer 1

The answer is "just one". If x = 0, y = -1. Otherwise,
Write the equation
as y+1 = x√2. Thus (y+1)/x = √2.
But that says that √2 is a rational number, which is false.

Answer 2

only the trivial solution (0,0) is the lattice point on this graph. an integer multiplied sqrt(2) is an irrational number. an irrational number minus an integer is still irrational.

Answer 3

If x is not 0, then no way. So there is just one point.