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Latest comment: 2 years ago2 comments2 people in discussion
The article contained (until I just removed it) a long section titled "Alternate form"
The section I just removed
The following discussion has been closed. Please do not modify it.
One may also reformulate Legendre's formula in terms of the base-p expansion of n. Let denote the sum of the digits in the base-p expansion of n; then
For example, writing n = 6 in binary as 610 = 1102, we have that and so
Similarly, writing 6 in ternary as 610 = 203, we have that and so
Proof
Write in base p. Then , and therefore
I have removed it because (1) it was completely uncited, and (2) I do not believe that this formula is referred to by anyone as "Legendre's formula", or as a form of Legendre's formula -- I think it's a totally separate formula for the same quantity. I would not object to restoring it, provided sources can be found that support the idea that this version is also known as Legendre's formula -- but if so, the proof should probably be removed (or at least abbreviated). --JBL (talk) 16:41, 12 March 2022 (UTC)Reply
"Alternate form" might not be the right section title, but I disagree that it doesn't belong in the article. The two formulas are not totally separate; they both show how depends on the base- representation of . They are equivalent and can be derived from each other. The section was only long because of the proof; if the proof is not necessary, let's leave it out. The citation should be the Moll reference, which says "An explicit expression for the error term was discovered by A. M. Legendre" and then immediately states a theorem that . Eric Rowland (talk) 21:39, 15 March 2022 (UTC)Reply