| Abstract: | We consider quadratic diophantine equations of the shape
 for a polynomial Q(X1, ..., Xs)  ZX1, ..., Xs] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s  3, the existence of a polynomialbound  s(H) with the following property: if equation (1) hasa solution x Zs at all, then it has one satisfying
 For s = 3 and s = 4 no polynomial bounds s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55. |
