Character sums and products of factorials modulo p

Products of Factorials Modulo p

The problem that we investigate in this note is the following: given p, find sufficient conditions that the parameters s and t should satisfy such as to ensure that Ps,t(p) contains the entire Zp. Let ε > 0 be any small number. Throughout this paper, we denote by c1, c2, . . . computable positive constants which are either absolute or depend on ε. From the way we formulated the above problem, w...

Binomial Character Sums modulo Prime Powers

We show that the binomial and related multiplicative character sums p ∑ x=1 (x,p)=1 χ(x(Ax +B)), p ∑ x=1 χ1(x)χ2(Ax k +B), have a simple evaluation for large enough m (for m ≥ 2 if p ABk).

Factorials as sums

Products of Three Factorials

We study a question of Erdős and Graham on products of three factorials being a square.

On Minimal Modulo 2 Sums of Products for Switching Functions