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A288104
Number of solutions to x^9 + y^9 = z^9 mod n.
9
1, 4, 9, 20, 25, 36, 55, 112, 189, 100, 121, 180, 109, 220, 225, 704, 289, 756, 487, 500, 495, 484, 529, 1008, 725, 436, 5103, 1100, 841, 900, 1081, 4864, 1089, 1156, 1375, 3780, 973, 1948, 981, 2800, 1681, 1980, 1513, 2420, 4725, 2116, 2209, 6336, 2989, 2900, 2601
OFFSET
1,2
COMMENTS
Equivalently, the number of solutions to x^9 + y^9 + z^9 == 0 (mod n). - Andrew Howroyd, Jul 17 2018
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Seiichi Manyama)
MATHEMATICA
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 *)
PROG
(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
(Python)
def A288104(n):
ndict = {}
for i in range(n):
m = pow(i, 9, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i+j) % n
if k in ndict:
count += ni*ndict[j]*ndict[k]
return count # Chai Wah Wu, Jun 05 2017
CROSSREFS
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).
Sequence in context: A288102 A288100 A063454 * A053807 A327238 A066109
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Jun 05 2017
EXTENSIONS
Keyword:mult added by Andrew Howroyd, Jul 17 2018
STATUS
approved