Abstract
Let Q (x) = Q (x(1), x(2), ..., x(n)) be a quadratic form with integer coefficients, p be an odd prime and parallel to x parallel to = max(i)vertical bar x(i)vertical bar : A solution of the congruence Q (x) equivalent to 0 (mod p(3)) is said to be a primitive solution if p inverted iota x(i) for some i. We prove that if p > A; where A = 5.2(41); then this congruence has a primitive solution, with parallel to x parallel to < 34p(3/2); provided that n >= 6 is even and Q is nonsinqular (modp). Moreover, similar result is proven for cube boxes centered at the origin with edges of arbitrary lengths. These two results are extension of the quadratic forms problems.