We obtain some theoretical and experimental results concerning various properties (the
number of fixed points, image distribution, cycle lengths) of the dynamical system naturally …

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 …

We determine the linear complexity of a family of p 2-periodic binary threshold sequences
derived from Fermat quotients modulo an odd prime p, where p satisfies 2^ p-1\not ≡ 1 (\rm …

We show that a p-ary polyphase sequence of period p 2 from the Fermat quotients is perfect.
That is, its periodic autocorrelation is zero for all non-trivial phase shifts. We call this Fermat …

We show that for any and a sufficiently large cube-free, any reduced residue class modulo
can be represented as a product of 14 integers from the interval. The length of the interval is …

We extend the definition of binary threshold sequences from Fermat quotients to Euler
quotients modulo pr with odd prime p and r⩾ 1. Under the condition of 2p− 1≢ 1 (modp2) …

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 use polynomial quotients modulo an odd prime p, which are generalized from the
Fermat quotients, to define two families of d (⩾ 2)-ary sequences of period p2. If d is a …

Given a prime p, we obtain upper bounds on single and bilinear character sums with Fermat
quotients q_p (u) ≡ u^ p-1-1 p (\rm mod\p),\quad0 ≦ q_p (u) ≦ p-1, where gcd (u, p)= 1. We …

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 …