# [seqfan] defn of A167415

Richard J. Mathar mathar at mpia-hd.mpg.de
Fri Jun 14 13:43:46 CEST 2019

```How is A167415 defined? It constructs solutions of A^2*(x+y)+3*x*y=0 (mod n)
and lists n such only the primitive solution (x=0,y=0)  exists.
Presumably A may be any non-zero (effectively: positive) integer (?).

Construct for example n=3, A=1, x=1, y=2 with 1^2*(1+2)+3*1*2 = 9 ==0 (mod 3)
and with that kind of definition, n=3 should not be in the sequence.

Construct for example n=6, A=1, x=2, y=4 with 1^2*(2+4)+3*2*4 = 30 ==0 (mod 6)
and with that kind of definition, n=6 should not be in the sequence.

I considered the idea that only nontrivial coprime (x,y) are allowed
but that does not resolve the case of n=3 as shown above , and also
not n=6 because
"n=", 6, "A=", 4, "x=", 1, "y=", 2, with 4^2*(1+2)+3*1*2=54 == 0 (mod 6)
works as counterexample.

Further restriction to coprime (A,x,y) does not work either. See
"n=", 13, "A=", 1, "x=", 1, "y=", 3, with 1^2*(1+3)+3*1*3 = 13 == 0 (mod 13).

Any ideas to elicidate the definition?

```