A271586 Number of squares in Z_n[i].

1, 2, 5, 4, 9, 10, 25, 8, 37, 18, 61, 20, 49, 50, 45, 24, 81, 74, 181, 36, 125, 122, 265, 40, 121, 98, 329, 100, 225, 90, 481, 88, 305, 162, 225, 148, 361, 362, 245, 72, 441, 250, 925, 244, 333, 530, 1105, 120, 1177, 242, 405, 196, 729, 658, 549, 200, 905, 450, 1741, 180, 961, 962, 925, 344, 441, 610, 2245

Offset

1,2

Comments

Equivalently, the number of distinct pairs (x^2-y^2, 2*x*y) mod n. - Andrew Howroyd, Aug 01 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

The squares in Z_3[i] are 0, i, 2i, 1 and 2, therefore a(3)=5.

Mathematica

GG[M_, s_] :=Table[Mod[(a +  b I)^s, M], {a, M}, {b, M}] // Flatten // Union // Length; Table[GG[M, 2], {M, 1, 144}]

Prog

(PARI) a(n)={my(v=vector(n)); for(i=0, n-1, for(j=0, n-1, my(k=(i^2-j^2)%n + 1); v[k]=bitor(v[k], 1<<((2*i*j)%n)))); sum(j=1, n, hammingweight(v[j]))} \\ Andrew Howroyd, Aug 01 2018

Crossrefs

Cf. A000224.

Sequence in context: A364035 A298011 A048678 * A278508 A296208 A324142

Adjacent sequences: A271583 A271584 A271585 * A271587 A271588 A271589

Keyword

nonn,mult

Author

José María Grau Ribas, Apr 10 2016

Extensions

Keyword:mult added by Andrew Howroyd, Aug 01 2018

Status

approved