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Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

Fix an integer ℓ ≥ 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order ℓ , where K satisfies some mild hypotheses. In this paper we define the family of generalized Rikuna polynomials { r n ( x , t ) } n ≥ 1 of degree ℓ n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd ℓ over an arbitrary base field and give applications to arithmetic dynamical systems.

Arithmetic properties of positive integers with fixed digit sum.

Florian Luca (2006)

Revista Matemática Iberoamericana

In this paper, we look at various arithmetic properties of the set of those positive integers n whose sum of digits in a fixed base b > 1 is a fixed positive integer s. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler φ function.

Currently displaying 1741 – 1760 of 1964