A197928 Number of pairs of integers i,j with 1<=i<=n, 1<=j<=i, such that i^2-j^2 = i*j (mod n).

1, 1, 1, 3, 3, 1, 1, 3, 6, 3, 11, 3, 1, 1, 3, 10, 1, 6, 19, 11, 1, 11, 1, 3, 15, 1, 6, 3, 29, 3, 31, 10, 11, 1, 3, 21, 1, 19, 1, 11, 41, 1, 1, 43, 24, 1, 1, 10, 28, 15, 1, 3, 1, 6, 53, 3, 19, 29, 59, 11, 61, 31, 6, 36, 3, 11, 1, 3, 1, 3, 71, 21, 1, 1, 15, 75, 11, 1, 79, 42, 45, 41, 1, 3, 3, 1, 29, 43, 89, 24, 1, 3, 31, 1, 93, 10, 1, 28, 96, 55, 101, 1, 1, 3, 3

Offset: 1

Author

John W. Layman, Oct 19 2011

Keywords

• nonn

Comments

It appears that, except for the first term, a(n)=n if and only if n is a prime congruent to 1 or 4 (mod 5).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A180783.

Programs

Maple

a:= n-> add(add(`if`(irem((i-j)*(i+j)-i*j, n)=0, 1, 0), j=1..i), i=1..n):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 19 2011