Properties of Modulo

Modulo has special properties that make calculations easier:

$\bullet$ $(a + b) \bmod m = ((a \bmod m) + (b \bmod m)) \bmod m$

$\bullet$ $(a \times b) \bmod m = ((a \bmod m) \times (b \bmod m)) \bmod m$

These let you take modulo at each step instead of waiting until the end. This prevents overflow when working with large numbers.