Currently displaying 1 – 17 of 17

Showing per page

Order by Relevance | Title | Year of publication

Reducibility and irreducibility of Stern ( 0 , 1 ) -polynomials

Karl DilcherLarry Ericksen — 2014

Communications in Mathematics

The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials a ( n ; x ) defined by a ( 0 ; x ) = 0 , a ( 1 ; x ) = 1 , a ( 2 n ; x ) = a ( n ; x 2 ) , and a ( 2 n + 1 ; x ) = x a ( n ; x 2 ) + a ( n + 1 ; x 2 ) ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that a ( n ; x ) can only have simple zeros, and we state a...

On a congruence of Emma Lehmer related to Euler numbers

John B. CosgraveKarl Dilcher — 2013

Acta Arithmetica

A congruence of Emma Lehmer (1938) for Euler numbers E p - 3 modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which E p - 3 0 ( m o d p ) play an important role, and we present some numerical results.

Page 1

Download Results (CSV)