A376646 Number of solutions to x + y == x^2 + y^2 (mod n) with x <= y.

1, 3, 3, 6, 3, 10, 5, 10, 7, 10, 7, 20, 7, 18, 10, 18, 9, 26, 11, 20, 18, 26, 13, 36, 11, 26, 19, 36, 15, 36, 17, 34, 26, 34, 18, 52, 19, 42, 26, 36, 21, 68, 23, 52, 26, 50, 25, 68, 29, 42, 34, 52, 27, 74, 26, 68, 42, 58, 31, 72, 31, 66, 50, 66, 26, 100, 35, 68, 50, 68

Offset: 1

Author

W. Edwin Clark, Sep 30 2024

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..4000

Programs

Maple

a:=proc(n)
 local x,y,count;
  count:=0:
  for x from 0 to n-1 do
   for y from x to n-1 do
     if (x+y) mod n =(x^2+y^2) mod n  then count:=count+1; fi;
   od:
  od:
  count;
end:
# second Maple program:
a:= n-> add(add(`if`(x^2-x+y^2-y mod n=0, 1, 0), x=0..y), y=0..n-1):
seq(a(n), n=1..70);  # Alois P. Heinz, Oct 01 2024

PARI

a(n) = sum(y=0, n-1, sum(x=0, y, (x+y) % n == (x^2+y^2) % n)); \\ Michel Marcus, Oct 01 2024

Python

def A376646(n):
    c = 0
    for x in range(n):
        m = x*(1-x)%n
        c += sum(1 for y in range(x,n) if y*(y-1)%n==m)
    return c # Chai Wah Wu, Oct 02 2024