For $x \in \mathbb{R}$, let $\{x\}=x-[x]$ denote the fractional part of $x$. Suppose $\mathcal{R}$ is a relation defined on $\mathbb{N}$ by $(a, b) \in \mathcal{R}$ if and only if $\left\{\frac{a^2}{8}\right\}=\left\{\frac{b^2}{8}\right\}$. Then the number of equivalence classes of $\mathcal{R}$ is

• A

  1
• B

  2
• Correct answer
  C

  3
• D

  8

Hence, the correct answer is option: 'C'.