A063454 Number of solutions to x^3 + y^3 = z^3 mod n.

1, 4, 9, 20, 25, 36, 55, 112, 189, 100, 121, 180, 109, 220, 225, 448, 289, 756, 487, 500, 495, 484, 529, 1008, 725, 436, 2187, 1100, 841, 900, 1081, 2048, 1089, 1156, 1375, 3780, 973, 1948, 981, 2800, 1681, 1980, 1513, 2420, 4725, 2116, 2209, 4032

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 25 2001

Keywords

• nonn
• mult

Comments

Equivalently, the number of solutions to x^3 + y^3 + z^3 == 0 (mod n). - Andrew Howroyd, Jul 18 2018

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..1000 from Seiichi Manyama)

Crossrefs

Number of solutions to x^k + y^k = z^k mod n: A062775 (k=2), this sequence (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), A288104 (k=9), A288105 (k=10).

Programs

PARI

a(n)={my(p=Mod(sum(i=0, n-1, x^(i^3%n)), 1-x^n)); polcoeff(lift(p^3), 0)} \\ Andrew Howroyd, Jul 18 2018

Python

def A063454(n):
    ndict = {}
    for i in range(n):
        m = pow(i,3,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 06 2017

Extensions

More terms from Dean Hickerson, Jul 26 2001