The title pretty much explains this question. I am wondering what the name for the lemma that states "If one integer divides two different integers then it will divide their difference." Is it alright for me to ask this on Math Stack Exchange, or is there a better place to ask it? Thank you in advance!

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    $\begingroup$ This would be like a [reference-request] question. That said, the lemma you mention does not, as far as I know, have "name" (nor does the generalization that any common divisor will divide any linear combination). The vast majority of results in mathematics do not have a "name" attached to them. $\endgroup$ Aug 5 at 19:50
  • $\begingroup$ Right on, thank you! So it is an acceptable question on the Math Stack Exchange forum if you ask it under a [reference-request] tag? @ArturoMagidin $\endgroup$
    – Simon Ward
    Aug 5 at 19:53
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    $\begingroup$ Yes (in my personal opinion); provide some context on why you need/want a name, and tag it [reference-request]. You could also indicate if a citation is enough, thought this particular one is in pretty much any standard number theory book. $\endgroup$ Aug 5 at 19:58
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    $\begingroup$ Merely to "ask it under a [reference-request] tag" does not make the Question acceptable. The Question should contribute to the mission of helping learners of math at some level, so your context (of why a name for a proposition is needed) is the most important aspect to make it acceptable. $\endgroup$
    – hardmath
    Aug 6 at 14:43
  • $\begingroup$ There is no standard name for the fact that the set of multiple multiples of $\,a\,$ is closed under differences (or any integer linear combinations). This is an immediate consequence of the linearity of the map $\,a\mapsto ax.\,$ Said more structurally, the set of all common multiples of some numbers are a prototypical example of an ideal ($R$-module). $\endgroup$ Aug 10 at 9:28
  • $\begingroup$ But you gave no context so it is not clear if this viewpoint is helpful at your knowledge level. At simpler levels it can be viewed as a special case of the Congruence Sum Rule (or the analogous Divisibility Sum Rule, e.g. see the Divisibility Product Rule). $\endgroup$ Aug 10 at 9:28

Yes, these questions are alright. You can use the tag . The description of this tag is-

This tag is for questions seeking external references (books, articles, etc.) about a particular subject.

So if you want to ask a question regarding the name of a lemma, just post it by starting the question with some background: why do you need the lemma name, what have you researched, and where are you stuck? Then the question would most likely be fine.

Here is a more detailed description of

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    $\begingroup$ It is also helpful to state why you think the lemma has a name. Most lemmas and theorems do not have names. $\endgroup$
    – user1729
    Aug 26 at 8:14
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    $\begingroup$ @user1729 Additionnally, the name is sometimes depending on the country (for instance Cauchy-Schwarz / Bunyakovsky inequality, or the squeeze theorem, which has many names, even in a single language), and it's not always named after the first who discovered or proved it: list of misnamed theorems $\endgroup$ Aug 26 at 10:55

I think such a question needs to justify its existence by stating why it is expected a name exists. If it does this, then it should be OK.

The issue is that most theorems (and almost all lemmas) do not have names - only the very famous ones do*. This means that these questions can be unanswerable: noone knows if a name exists, but noone is confident enough to say "there is no name".

*Naming theorems can result in confusion: As Jean-Claude Arbaut pointed out in the comments to the other answer, some theorems have multiple names, such as the squeeze theorem, while some names refer to multiple theorems, like "Cauchy's Theorem". Some results are even miss-attributed, for example people still refer to The Lemma That Is Not Burnside's as "Burnside's Lemma", including Wikipedia.


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