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A288104 Number of solutions to x^9 + y^9 = z^9 mod n.

%I A288104 #20 Jul 18 2018 02:19:22
%S A288104 1,4,9,20,25,36,55,112,189,100,121,180,109,220,225,704,289,756,487,
%T A288104 500,495,484,529,1008,725,436,5103,1100,841,900,1081,4864,1089,1156,
%U A288104 1375,3780,973,1948,981,2800,1681,1980,1513,2420,4725,2116,2209,6336,2989,2900,2601
%N A288104 Number of solutions to x^9 + y^9 = z^9 mod n.
%C A288104 Equivalently, the number of solutions to x^9 + y^9 + z^9 == 0 (mod n). - _Andrew Howroyd_, Jul 17 2018
%H A288104 Chai Wah Wu, <a href="/A288104/b288104.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Seiichi Manyama)
%t A288104 Table[cnt=0; Do[If[Mod[x^9 + y^9 - z^9, n]==0, cnt++], {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; cnt, {n, 50}] (* _Vincenzo Librandi_, Jul 18 2018 *)
%o A288104 (PARI) a(n)={my(p=Mod(sum(i=0, n-1, x^lift(Mod(i,n)^9)), 1-x^n)); polcoeff(lift(p^3), 0)} \\ _Andrew Howroyd_, Jul 17 2018
%o A288104 (Python)
%o A288104 def A288104(n):
%o A288104     ndict = {}
%o A288104     for i in range(n):
%o A288104         m = pow(i,9,n)
%o A288104         if m in ndict:
%o A288104             ndict[m] += 1
%o A288104         else:
%o A288104             ndict[m] = 1
%o A288104     count = 0
%o A288104     for i in ndict:
%o A288104         ni = ndict[i]
%o A288104         for j in ndict:
%o A288104             k = (i+j) % n
%o A288104             if k in ndict:
%o A288104                 count += ni*ndict[j]*ndict[k]
%o A288104     return count # _Chai Wah Wu_, Jun 05 2017
%Y A288104 Number of solutions to x^k + y^k = z^k mod n: A062775 (k=2), A063454 (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), this sequence (k=9), A288105 (k=10).
%K A288104 nonn,mult
%O A288104 1,2
%A A288104 _Seiichi Manyama_, Jun 05 2017
%E A288104 Keyword:mult added by _Andrew Howroyd_, Jul 17 2018