# [seqfan] Re: In the vein of 103314

Max Alekseyev maxale at gmail.com
Thu Dec 21 07:57:35 CET 2017

```Robert - yes, I agree.
It may be worth also to consider other number of terms in the sum, giving
raise to the table:
1,
1, 3,
1, 4, 10,
1, 5, 15, 25,
1, 6, 21, 56, 126,
1, 7, 28, 64, 100, 127,
1, 8, 36, 120, 330, 792, 1716,
1, 9, 45, 165, 495, 825, 1365, 2241,
1, 10, 55, 220, 715, 2002, 5005, 9724, 18469,

The proposed sequence forms the main diagonal in this table.

Regards,
Max

On Wed, Dec 20, 2017 at 1:06 PM, <israel at math.ubc.ca> wrote:

> But the primitive roots are zeros of a polynomial of degree phi(n), namely
> the n'th cyclotomic polynomial. So they are not all distinct.
>
> Cheers,
> Robert
>
>
> On Dec 20 2017, Max Alekseyev wrote:
>
> They all must be distinct as otherwise the n-th primitive root would be a
>> zero of a polynomial of degree n-1.
>> Hence, there are binomial(k+n-1,n-1) distinct values of k-term sums of nth
>> roots of 1, for any k>=1.
>>
>> Regards,
>> Max
>>
>> On Tue, Dec 19, 2017 at 4:24 PM, David Wilson <davidwwilson at comcast.net>
>> wrote:
>>
>> How many distinct values are taken on by a sum of n nth roots of 1?
>>>
>>>
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
```