What verb should I use for this "mod" operation, e.g. $21=5z+7y\implies1\equiv2y\pmod 5$.

Question

What verb should I use for this operation below? $$21=5z+7y\implies1\equiv2y\pmod 5$$

Can I just say "mod 5" on both sides? After all "mod" as a math term is not included in an English dictionary, so I am really not sure how to use it in a sentence. And please provide other ways to describe this if possible.

Answer 1

I believe the conventional way to read the operation is "reduce modulo $5$"; for instance,

• "Given $21=5z+7y$, we can reduce modulo $5$ to obtain $1\equiv 2y$."
• "The relation $21=5z+7y$, reduced modulo $5$, yields $1\equiv 2y$."

Informally, you could say "modding by $5$", which is about on the order of saying "square-rooting". You wouldn't want to put this in a scholarly paper, but a lecture audience would understand you.

Answer 2

I think it's fine as it stands (that is, when you display the entire implication in a single line). Then it makes the $\pmod 5$ cover the entire expression. The meaning would then be clear.

Answer 3

twenty-one being of form five times x plus seven times y, implies that, 1 is the remainder on division by five of two times y .

Google states:

mod2 /mäd/ preposition MATHEMATICS preposition: mod another term for modulo.