Problem 372

Pencils of rays

Let R(`M`, `N`) be the number of lattice points (`x`, `y`) which satisfy `M``x``N`, `M``y``N` and is odd.

We can verify that R(0, 100) = 3019 and R(100, 10000) = 29750422.

Find R(2·10^{6}, 10^{9}).

__ Note__: represents the floor function.

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