As is well known, for two odd prime numbers p and q, the Legendre symbol (p/q) describes the decomposition law of q in the quadratic extension Q([square root of p])/Q.
Redei ([R]) introduced a certain triple symbol with the intension of a generalization of the Legendre symbol and Gauss' genus theory.
denotes the Legendre symbol
, then x + y could never take the value 0.
Suppose that p is a prime such that (d/p) = 1, where (d/p) is the Legendre symbol
where (x=p) denotes the Legendre symbol and m = (p + 1)=2.
where (a=p) = [chi square](a) is the Legendre symbol modulo p.
Sun["Quartic residues and binary qudratic forms", Journal of Number Theory, 2005, 113(1)] conjectured that: Let p and q be the primes of the form 4k + 1 such that (p/q) = 1, where (p/q) is the Legendre symbol
, then [h.