A062775, related to pythagorean triples mod n / reviewed and collected materials

[Gottfried Helms]

Am 19.12.03 15:39 schrieb Gottfried Helms:
> 
> 
> Appendix: reference for the sequence A
> 
> 
>>---------------------------------
>>||> ID Number: A062775
>>||> URL:       http://www.research.att.com/projects/OEIS?Anum=A062775
>>||>
>>||> Sequence:  1,4,9,24,25,36,49,96,99,100,121,216,169,196,225,448,289,
>>||>            396,361,600,441,484, 529,864,725,676,891,1176,841,900,961,
>>||>            1792,1089,1156, 
>>1225,2376,1369,1444,1521,2400,1681,1764,1849,
>>||>            2904,2475,2116,2209,4032,2695,2900
>>||>
>>||> Name:      Number of Pythagorean triples mod n; i.e. number of 
>>non-congruent
>>||>            solutions to x^2 + y^2 = z^2 mod n.
>>||>
>>||> Comments:  a(n) is multiplicative and for a prime p: a(p) = p^2.
>>||>
>>||>The starting number of this series is 1.
>>
>>Anonymous wrote:
>>
>> > I've noticed that when the moebius function of n is either -1 or 
>>+1,then the
>> > series term is n^2.  However when the moebius(n) = 0,then the 
>>interesting set
>> > of numbers that I've given results.
> 
Hi Seqfans -

 caused by a request from sci.math.research I stepped into this
 subject again, reviewed and collected my material on that problem,
 and added some new material for the problem with higher exponents.

 I compiled this stuff at

  http://www.uni-kassel.de/~helms/priv/math/

 (see the link at the index there)

 Any comments are welcome; the related sequences in OEIS could
 be extended (or created) by data from this review-process.
 Since I cannot guess, whether these are trivia or not, I ask
 here, whether the OEIS/some Seqfans might be interested?

Regards-

Gottfried Helms