Throughout my education in computer science, I feel like I've heard the terms modulo and modulus used interchangeably.  It looks like even Wikipedia claims that modulo is sometimes called 'modulus' (see the first sentence of the page on 'modulo').I've looked into this issue a little and it seems that modulo finds singular use in modular arithmetic (e.g. 19 and 64 are congruent modulo 5).  In addition, I've seen the symbol % be referred to as modulo.Meanwhile, modulus appears to have several definitions, including absolute value and constant factor as well as referring to the 5 in modulo 5.Is it ever correct to use these terms interchangeably in the context of computer science?  Are they simply different types of words that represent the same idea (such as run and runner)?  Are there important differences in other disciplines?Bonus: Etymologically, what gave rise to these two terms?
What is the difference between modulo and modulus?
terminology;modular arithmetic
modulo is an operator.  For instance, we might say 19 and 64 are congruent modulo 5.modulus is a noun.  It describes the 5 in modulo 5.  We might say the modulus is 5.No, the two should not be used interchangeably.  It would be incorrect to say 19 and 64 are congruent modulus 5.  It would also be incorrect to the modulo is 5.See also https://en.wikipedia.org/wiki/Modular_arithmetic and https://en.wikipedia.org/wiki/Modulo_operation.  Both define the word modulus, and as far as I can see they use it correctly.