Let a1,...,an be n(³ 2) nonzero integers such that the diagonal quadratic equationis solvable in integers x1,...,xn not all zero. It is shown that (1) has a solution in integers x1,...,xn satisfying
a1x21 +¼+ anx2n = 0 (1) The inequality (2) is best possible. This is joint work with Zhiming Ou.
0 < |a1| x21 +¼+ |an |x2n £ 2 |a1¼an|. (2)