Gaussian elimination can be used to solve a system of linear equations modulo a prime p.
$p=2$ is trivial because no division is ever needed (only $\oplus$ operations).
However, for $p=3$ it seems that I require fractions. For example:
$2X + 2Y + Z = 1 ≡ 3$
To have row reduced form I need the coefficient next to X to be equal to 1. If I divide by 2, then the value on the right becomes 1/2.
Am I missing a simpler way?
In any field, division by $x$ is the same as multiplication by $x^{-1}$. The integers modulo prime $p$ form a field.