## Let $R(M, N)$ be the number of lattice points $(x, y)$ which satisfy $M\!\lt\!x\!\le\!N$, $M\!\lt\!y\!\le\!N$ and $\large\left\lfloor\!\frac{y^2}{x^2}\!\right\rfloor$ is odd.

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

Find $R(2\cdot10^6, 10^9)$.

Note: $\lfloor x\rfloor$ represents the floor function.

### The function $R(M, N)$ counts the number of lattice points $(x, y)$, where $x$ and $y$ are integers, such that $M
Firstly, $\lfloor\frac{y^2}{x^2}\rfloor$ is odd if and only if $x^2More Answers:

BadugiFirstly, $\lfloor\frac{y^2}{x^2}\rfloor$ is odd if and only if $x^2

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