Fermat's little theorem

Let $p$ be a prime and $a$ any integer. Show that
$$a^p\equiv a(\mathrm{mod}p).$$

It can be proved by induction with the binomial theorem, by counting coloured necklaces, and by noticing that multiplying by $a$ shuffles the non-zero residues. Which of these would you hand to someone who had never seen modular arithmetic?