CAT 2015 Quantitative Ability

$\mathit{x}=\left({106}^{90}-{49}^{90}\right)$
$\left({\mathit{x}}^{\mathit{n}}-{\mathit{a}}^{\mathit{n}}\right)$ is divisible by both (x - a) and (x + a) whenever n is even
⇒ $\left({106}^{90}-{49}^{90}\right)$ is divisible by both 57 and 155
57 = 19 x 3
155 = 31 x 5
∴ $\left({106}^{90}-{49}^{90}\right)$ will be divisible by (19 x 31) = 589 as well.
Also, note that $\left({106}^{90}-{49}^{90}\right)$ will be odd and options (b) and (c) are even. Hence, they can be rejected