We prove a bound on sums of products of multiplicative characters of shifted Fermat
quotients modulo p. From this bound we derive results on the pseudorandomness of …

We describe the trace representations of two families of binary sequences derived from the
Fermat quotients modulo an odd prime p (one is the binary threshold sequences and the …

For a prime p and an integer u with gcd (u, p)= 1, we define Fermat quotients by the
conditions Heath-Brown has given a bound of exponential sums with N consecutive Fermat …

We give the trace representation of a family of binary sequences derived from Euler
quotients by determining the corresponding defining polynomials. The result extends an …

We investigate the $ k $-error linear complexity of $ p^ 2$-periodic binary sequences
defined from the polynomial quotients (including the well-studied Fermat quotients), which is …

We study the distribution of s-dimensional vectors of consecutive Euler–Fermat quotients
modulo a composite m. More precisely, we prove two different discrepancy bounds for s= 1 …

Let p be a prime, f (X)∈ Z [X] with leading coefficient not divisible by p, and R a complete
residue system modulo p. For an integer u we define the polynomial quotient qf, p, R (u) by f …

For a given polynomial P(X) of degree d≥1 modulo p, we estimate the number of elements
1≤u<p for which P(u) coincides with the Fermat quotient q_p(u) modulo p. In particular, the …

The Euler quotient modulo an odd-prime power $ p^ r~(r> 1) $ can be uniquely decomposed
as a $ p $-adic number of the form $$\frac {u^{(p-1) p^{r-1}}-1}{p^ r}\equiv a_0 (u)+ a_1 (u) …

Let p be an odd prime and be a positive integer. The authors<? show [AQ ID= Q1]?>
continue to investigate the binary sequence over defined from polynomial quotients by …