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Displaying 41 – 60 of 92

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On semiregular digraphs of the congruence x k y ( mod n )

Lawrence Somer, Michal Křížek (2007)

Commentationes Mathematicae Universitatis Carolinae

We assign to each pair of positive integers n and k 2 a digraph G ( n , k ) whose set of vertices is H = { 0 , 1 , , n - 1 } and for which there is a directed edge from a H to b H if a k b ( mod n ) . The digraph G ( n , k ) is semiregular if there exists a positive integer d such that each vertex of the digraph has indegree d or 0. Generalizing earlier results of the authors for the case in which k = 2 , we characterize all semiregular digraphs G ( n , k ) when k 2 is arbitrary.

On sums of binomial coefficients modulo p²

Zhi-Wei Sun (2012)

Colloquium Mathematicae

Let p be an odd prime and let a be a positive integer. In this paper we investigate the sum k = 0 p a - 1 ( h p a - 1 k ) ( 2 k k ) / m k ( m o d p ² ) , where h and m are p-adic integers with m ≢ 0 (mod p). For example, we show that if h ≢ 0 (mod p) and p a > 3 , then k = 0 p a - 1 ( h p a - 1 k ) ( 2 k k ) ( - h / 2 ) k ( ( 1 - 2 h ) / ( p a ) ) ( 1 + h ( ( 4 - 2 / h ) p - 1 - 1 ) ) ( m o d p ² ) , where (·/·) denotes the Jacobi symbol. Here is another remarkable congruence: If p a > 3 then k = 0 p a - 1 ( p a - 1 k ) ( 2 k k ) ( - 1 ) k 3 p - 1 ( p a / 3 ) ( m o d p ² ) .

On the basic character of residue classes.

Peter J. Hilton, Jennifer Hooper, Jean Pedersen (1989)

Publicacions Matemàtiques

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...

On the correlation of families of pseudorandom sequences of k symbols

Kit-Ho Mak, Alexandru Zaharescu (2016)

Acta Arithmetica

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