Modular equivalence

"Congruent to modulo \(N\)" is a relation on numbers.

Most relations are expressed with a symbol between the two sides of the relation. Modular equivalence needs somewhere for the parameter to go. Conventionally, it's written on the right:

\[ 7 \equiv 1 \mod 3 \]

Sometimes there are brackets around the mod part:

\[ 7 \equiv 1 \pmod 3 \]

The spacing before 'mod' seems to be important, to

This makes it hard to chain equivalence relations:

\[ 27 \equiv 12 \pmod {15} \equiv 3 \pmod 4 \]

Or, without brackets:

\[ 27 \equiv 12 \bmod {15} \equiv 3 \bmod 4 \]