On the Congruence ∑ aixik = 0(mod p)

Let p denote a prime, a_i≠O (modp) for 1 < i < S. From a wellknown theorem of Chevalley [1] it follows that the congruence in the title has a non-trivial solution (i.e. one in which not all x_i s are multiples of p) if S > k + 1.