(I bet you will send me to english.stackexchange.com and they will send me back here)

I will use an example - I have two lists of integers:

  • list A: 0, 4, 8, 12, ...
  • list B: 2, 6, 10, 14, ...

I'm looking for a neat word to clearly differentiate these lists when talking to a colleague who doesn't really have a maths mindset. My intuition is:

  • list A is "even multiples of 2"
  • list B is "odd multiples of 2"

I tried to google this sort of wording, but I get mixed results:

  • Some results use these words the way I came up with, which is promising;
  • Some results would only call n and odd multiple of k if n itself is an odd number (and thus k is odd too);
  • Some results also use the word "odd" as another word for "unusual" (which is odd, haha)

So what is the term for multiples made by using an odd/even factor?

Hopefully by now you can see why I struggled to come up with a good title for this question.

EDIT: A comment from GerryMyerson hints that I probably used an unfortunate k in my example. I'm after a word that will work for any k, whether or odd or even (although "pateksan's odd multiples" of odd k are actually odd numbers). So for example list A might be 0, 8, 16, 24, ... and list B might be 4, 12, 20, 28, ...

  • 1
    $\begingroup$ The first set is $4\mathbb{Z}$ and the next one is $4 \mathbb{Z}+2.$ Or replace $\mathbb{Z}$ with $\mathbb{N}_0$ if you only want non-negative integers. $\endgroup$ – K.defaoite Jul 24 '20 at 2:35
  • 1
    $\begingroup$ Perhaps "non negative numbers that are multiples of four" and "non negative numbers that leave a remainder of two on division by four"? $\endgroup$ – K.defaoite Jul 24 '20 at 2:40
  • 1
    $\begingroup$ $A$ is doubly even numbers, $B$ is singly even numbers. Sez en.wikipedia.org/wiki/Singly_and_doubly_even $\endgroup$ – Gerry Myerson Jul 24 '20 at 2:43
  • 1
    $\begingroup$ @Don I won't disagree with you, but OP asked "what is the term...?" and insofar as there is a term this seems to be it. $\endgroup$ – Gerry Myerson Jul 24 '20 at 2:52
  • 1
    $\begingroup$ If that's what you want, pateksan, then that's what you should ask for. We're mathematicians here, not mindreaders. $\endgroup$ – Gerry Myerson Jul 24 '20 at 2:53

We use the term modulo to describe what is left when you divide integers by a number $m$. Your example of $0,4,8,12,\ldots$ are the numbers equivalent to $0$ modulo $4$, often written $n \equiv 0 \pmod 4$. The numbers $2,6,10,14,\ldots$ are equivalent to $2 \pmod 4$. Does that do what you want?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.