The distribution of solutions of the congruence x1x2x3...xnc (mod p)

For a cube B of size B, we obtain a lower bound on B so that B boolean AND V is nonempty, where V is the algebraic subset of F-p(n) defined by x(1)x(2)x(3) ... x(n) = c (mod p), n a positive integer and c an integer not divisible by p. For n = 3 we obtain that B boolean AND V is nonempty if B >> p(2/3) (log p)(2/3), for n = 4 we obtain that B boolean AND V is nonempty if B >> root p log p, and for n greater than or equal to 5 we obtain that B boolean AND V is nonempty if B >> p(1/4 + 1/root 2(n+4)) (log p)(3/2). Using the assumption of the Grand Riemann Hypothesis we obtain B boolean AND V is nonempty if B >>(epsilon) p(2/n+epsilon).