The symbol $\mid$ reads as "divides", and $\nmid$ as "does not divide". For instance, $2 \: \mid \:6$ and $2 \: \nmid \: 5$ are both true. Consider the following statements.
- There exists a positive integer $a$ such that $(2 \mid (a^3 -1))$ and $( 2 \mid a)$.
- There exists a positive integer $b$ such that $6 \nmid (b^3 -b)$.
What can you say about these statements?
- Only i is true
- Only ii is true
- Both i and ii are true
- Neither i nor ii is true