Modular equivalence
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"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:
\[ 27 \equiv 12 \bmod {15} \equiv 3 \bmod 4 \]
