Talk:P-adic Valuation of Difference of Powers with Coprime Exponent

This result is sufficiently interesting in itself, because it works for all $p$, including $p=2$, whereas there is no version of LTE for $p=2$ under the weak assumption that $2\mid x-y$.

In short, I suggest to put this on its own page. I'm thinking of Not Lifting The Exponent Lemma. This name is not commonly used, but it says what it is. --barto (talk) 15:17, 23 August 2017 (EDT)

But maybe there's a less joky name, apart from P-adic Valuation of Difference of Powers with Exponent not Divisible by Prime. --barto (talk) 16:01, 23 August 2017 (EDT)


 * I've never been particularly happy with the name "lifting the exponent lemma", but since it seems to be generally used in the literature (is it, though, apart from Parvardi's paper?), because it does not really describe what it does. But it's out there, it's short and specific, so no worries.


 * So, how about: P-adic Valuation of Difference of Powers with Coprime Exponent?


 * While I'm here, what I do have a problem with is that "$p$-adic valuation" page -- it took me a while to work out that it is in fact the same thing as what I called Definition:Multiplicity of Prime Factor when I first came into this area and could not find its name (that's the trouble with being self-taught, you tend not to get told the proper names for things). This will have to be revisited, of course.


 * Is it advisable to put a note into Definition:P-adic Valuation to "dumb it down" so as to make it clear that it means: the highest power of $p$ that divides a number? Then it's high-school accessible, which is often a level at which certain aspects of number theory are introduced in the context of recreational mathematics. --prime mover (talk) 03:14, 24 August 2017 (EDT)


 * On the name "LTE": It does not have a name outside the olympiad world, where everyone knows it by this name. I don't think that paper coined it, but it is quite modern. I expect it to be somewhat more commonly used when the current olympiad generation starts doing research. --barto (talk) 04:04, 24 August 2017 (EDT)


 * P-adic Valuation of Difference of Powers with Coprime Exponent is fine for me. --barto (talk) 04:04, 24 August 2017 (EDT)


 * For the discussion on $p$-adic valuation, let's continue at Definition talk:P-adic Valuation. --barto (talk) 04:04, 24 August 2017 (EDT)