Talk:AKS test for primes: Difference between revisions

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Revision as of 17:10, 7 February 2014

Combinations

There is a link between the coefficients of the expansion of $(x-1)^{p}$ and nCr. --Paddy3118 (talk) 20:56, 6 February 2014 (UTC)

Lower Limit

Again... 1 appears as an "is it prime, isn't it prime" candidate.

$1$ is prime if all the coefficients of the polynomial expansion of: $(x-1)^{p}-(x^{p}-1)$ are divisible by $p$ . All the coefficients is the empty set. 1 is divisible by absolutely everything in the empty set. Is there a better wording out there? (That doesn't include the phrases "any number not 1" or "any number > 1")

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 ==Combinations==
 There is a link between the coefficients of the expansion of <math>(x-1)^p</math> and nCr. --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 20:56, 6 February 2014 (UTC)
+==Lower Limit==
+Again... 1 appears as an "is it prime, isn't it prime" candidate.
+<math>1</math> is prime if all the coefficients of the polynomial expansion of: <math>(x-1)^p - (x^p - 1)</math>
+are divisible by <math>p</math>. All the coefficients is the empty set. 1 is divisible by absolutely everything in the empty set. Is there a better wording out there? (That doesn't include the phrases "any number not 1" or "any number > 1")