A288105 Number of solutions to x^10 + y^10 = z^10 mod n.

1, 4, 9, 24, 25, 36, 49, 192, 99, 100, 201, 216, 169, 196, 225, 1024, 289, 396, 361, 600, 441, 804, 529, 1728, 3125, 676, 1377, 1176, 841, 900, 601, 6144, 1809, 1156, 1225, 2376, 1369, 1444, 1521, 4800, 1201, 1764, 1849, 4824, 2475, 2116, 2209, 9216, 2695, 12500

Offset

1,2

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^10 + y^10 - z^10, n]==0, cnt++], {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; cnt, {n, 50}] (* Vincenzo Librandi, Jul 18 2018 *)

Prog

(Python)
def A288105(n):
    ndict = {}
    for i in range(n):
        m = pow(i, 10, 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), A288104 (k=9), this sequence (k=10).

Sequence in context: A272252 A067801 A062775 * A288101 A320913 A329879

Adjacent sequences: A288102 A288103 A288104 * A288106 A288107 A288108

Keyword

nonn,mult

Author

Seiichi Manyama, Jun 05 2017

Extensions

Keyword:mult added by Andrew Howroyd, Jul 17 2018

Status

approved