The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . The digraph is semiregular if there exists a positive integer such that each vertex of the digraph has indegree or 0. Generalizing earlier results of the authors for the case in which , we characterize all semiregular digraphs when is arbitrary.
Let p be an odd prime and let a be a positive integer. In this paper we investigate the sum , where h and m are p-adic integers with m ≢ 0 (mod p). For example, we show that if h ≢ 0 (mod p) and , then
,
where (·/·) denotes the Jacobi symbol. Here is another remarkable congruence: If then
.
Let t, b be mutually prime positive integers. We say that the residue class t mod b is basic if there exists n such that tn ≡ -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy p ≡ 3 mod 4, then t is basic mod b if t is a quadratic non-residue mod p for all such p; and t is not basic mod b if t is a quadratic residue mod p for all such p. If, for all prime factors...
In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.
Currently displaying 41 –
60 of
92