Displaying similar documents to “Multiplicative functions and k -automatic sequences”

On a kind of generalized Lehmer problem

Rong Ma, Yulong Zhang (2012)

Czechoslovak Mathematical Journal

Similarity:

For 1 c p - 1 , let E 1 , E 2 , , E m be fixed numbers of the set { 0 , 1 } , and let a 1 , a 2 , , a m ( 1 a i p , i = 1 , 2 , , m ) be of opposite parity with E 1 , E 2 , , E m respectively such that a 1 a 2 a m c ( mod p ) . Let N ( c , m , p ) = 1 2 m - 1 a 1 = 1 p - 1 a 2 = 1 p - 1 a m = 1 p - 1 a 1 a 2 a m c ( mod p ) ( 1 - ( - 1 ) a 1 + E 1 ) ( 1 - ( - 1 ) a 2 + E 2 ) ( 1 - ( - 1 ) a m + E m ) . We are interested in the mean value of the sums c = 1 p - 1 E 2 ( c , m , p ) , where E ( c , m , p ) = N ( c , m , p ) - ( ( p - 1 ) m - 1 ) / ( 2 m - 1 ) for the odd prime p and any integers m 2 . When m = 2 , c = 1 , it is the Lehmer problem. In this paper, we generalize the Lehmer problem and use analytic method to give an interesting asymptotic formula of the generalized Lehmer problem.

The cubic mapping graph for the ring of Gaussian integers modulo n

Yangjiang Wei, Jizhu Nan, Gaohua Tang (2011)

Czechoslovak Mathematical Journal

Similarity:

The article studies the cubic mapping graph Γ ( n ) of n [ i ] , the ring of Gaussian integers modulo n . For each positive integer n > 1 , the number of fixed points and the in-degree of the elements 1 ¯ and 0 ¯ in Γ ( n ) are found. Moreover, complete characterizations in terms of n are given in which Γ 2 ( n ) is semiregular, where Γ 2 ( n ) is induced by all the zero-divisors of n [ i ] .

Tribonacci modulo 2 t and 11 t

Jiří Klaška (2008)

Mathematica Bohemica

Similarity:

Our previous research was devoted to the problem of determining the primitive periods of the sequences ( G n mod p t ) n = 1 where ( G n ) n = 1 is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime p 2 , 11 . In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes p = 2 , 11 .

A new efficient presentation for P S L ( 2 , 5 ) and the structure of the groups G ( 3 , m , n )

Bilal Vatansever, David M. Gill, Nuran Eren (2000)

Czechoslovak Mathematical Journal

Similarity:

G ( 3 , m , n ) is the group presented by a , b a 5 = ( a b ) 2 = b m + 3 a - n b m a - n = 1 . In this paper, we study the structure of G ( 3 , m , n ) . We also give a new efficient presentation for the Projective Special Linear group P S L ( 2 , 5 ) and in particular we prove that P S L ( 2 , 5 ) is isomorphic to G ( 3 , m , n ) under certain conditions.