- (i) Determine all the possible integers \(a\), where \(a > 3\), such that
$$15 \equiv 3 \bmod a$$
(ii) Show that if \(p\) is prime, \(x\) is an integer and \(x ^ { 2 } \equiv 1 \bmod p\) then either
$$x \equiv 1 \bmod p \quad \text { or } \quad x \equiv - 1 \bmod p$$
(iii) A company has \(\pounds 13940220\) to share between 11 charities.
Without performing any division and showing all your working, decide if it is possible to share this money equally between the 11 charities.