ON DIOPHANTINE EQUATIONS INVOLVING SUMS OF POWERS WITH QUADRATIC CHARACTERS AS COEFFICIENTS .2.

Let d be the discriminant of a quadratic field. Denote by (d/., h(d) a nd k(2)(d) the Kronecker symbol, the class number and the order of the K-2-group of the ring of integers of a quadratic field with the discr iminant d, respectively.In this paper we shall be concerned with the e quation (d/1) 1(k) + (d/2) 2(k) +...+ (d/xd) (xd)(k) = by(z) in the ca se of positive d. Using methods of [8] (based on the concept of [9]) w e shall prove the above equation has only finitely many solutions in i ntegers x greater than or equal to, 1, y, z > 1 (with effective upper bounds for them), if b not equal 0, k greater than or equal to 6 are i ntegers and 2 inverted iota d, 32 inverted iota k(2)(d). Moreover it i s proved for all d satisfying 32 inverted iota k(2)(d) provided k and d are of different parities.