Hi T.Rex!

For prime

with

(and q>1) your conjecture is true: Because of the quadratic reciprocity law (Gauß) 5 is a quadratic residue of

, iff

is quadratic residue of 5 (because both are of the from 4n+1). But

so 5 is a quadratic residue of

and there existists two numbers X and Y, which have the properties

and

Yours,

Cyrix