[seqfan] Re: A180634

[Neil Sloane]

I've taken the liberty of expanding the comments in A180634 to include
more remarks from those two emails.
Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Mon, Dec 8, 2014 at 9:39 PM, W. Edwin Clark <wclark at mail.usf.edu> wrote:
> I think it is true. Assume n > 2.
>
> Use Gauss's generalization of Wilson's theorem
> <http://en.wikipedia.org/wiki/Wilson%27s_theorem#Gauss.27s_generalization>,
> namely, the product of the units of Z_n is -1 if n is 4 or p^i or 2p^i for
> odd primes p, i >0,  and
> is equal to 1 otherwise.
>
> And assume that the comments and formula for A033949 are correct.
>
>
> On Mon, Dec 8, 2014 at 7:11 PM, <israel at math.ubc.ca> wrote:
>
>> A180634 is "Numbers n such that the discriminant of the n-th cyclotomic
>> polynomial is a square". It appears to also coincide with n such that the
>> product of elements in the group of invertible elements mod n (i.e. the
>> product mod n of x such that 1 <= x < n and x is coprime to n) is 1. Is
>> this true? An equivalent characterization of the latter (apart from n=2): n
>> such that the number of square roots of 1 mod n is divisible by 4.
>>
>> Cheers,
>> Robert
>>
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