A182158 Number of solutions to x^2 + x + y + y^2 == 1 mod n.

1, 0, 1, 0, 4, 0, 8, 0, 0, 0, 12, 0, 12, 0, 4, 0, 16, 0, 20, 0, 8, 0, 24, 0, 20, 0, 0, 0, 28, 0, 32, 0, 12, 0, 32, 0, 36, 0, 12, 0, 40, 0, 44, 0, 0, 0, 48, 0, 56, 0, 16, 0, 52, 0, 48, 0, 20, 0, 60, 0, 60, 0, 0, 0, 48, 0, 68, 0, 24, 0, 72, 0, 72, 0, 20, 0, 96, 0

Offset

1,5

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

a[1]=1; a[n_]:=Length@Rest@Union@Flatten@Table[If[Mod[i^2+i+ j +j^2 , n]==1, i+I j, 0], {i, 0, n-1}, {j, 0, n-1}]; Table[a[n], {n, 1, 98}]

Prog

(PARI) a(n)=sum(x=1, n, sum(y=1, n, Mod(x^2+x+y+y^2, n)==1)) \\ Charles R Greathouse IV, Apr 16 2012
(PARI) A(n)=my(v=vecsort(vector(n, i, i^2+i)%n), u=vecsort(v, , 8), w=vector(#u), j=1); w[1]=1; for(i=2, #v, if(v[i]>v[i-1], j++); w[j]++); sum(i=2, #u, while(u[i]+u[j]>n+1, j--); if(u[i]+u[j]==n+1, w[i]*w[j]))+ if(#u>1&&u[2]==1, 2*w[1]*w[2])
a(n)=n=factor(n); prod(i=1, #n[, 1], A(n[i, 1]^n[i, 2])) \\ Charles R Greathouse IV, Apr 16 2012
(Magma) [n eq 1 select 1 else #[x: x in [1..n], y in [1..n] | (x^2+x+y+y^2) mod n eq 1]: n in [1..78]]; // Bruno Berselli, Apr 16 2012

Crossrefs

Sequence in context: A200501 A141433 A019111 * A103554 A261278 A340424

Adjacent sequences: A182155 A182156 A182157 * A182159 A182160 A182161

Keyword

nonn,mult

Author

José María Grau Ribas, Apr 15 2012

Status

approved