Talk:AKS test for primes

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") Tim-brown

It could also be worded that there isn't any number in the empty set that is divisible by $1$. I think 1 should simply be ignored Denommus

If you can "sweep it under the carpet" then why not? It is a small part of the task. --Paddy3118 (talk) 19:34, 7 February 2014 (UTC)

It would't be the first time a primality test has had some weird edge cases. (What about negative numbers? They'd need infinite polynomial expansions…) –Donal Fellows (talk) 21:55, 7 February 2014 (UTC)