How to use "mod" related words in technical paper？
A modular operation is an operation done modulo some modulus.


"modular" is an adjective: modular inverse, modular operation, modular reduction, ...
"modulo" is indeed the Latin ablative of modulus, and that makes it an adverb: I walk modulo $n$, just like I walk fast.
"modulus" is a noun: the number $n$ is the modulus that you would use in some system.