Bull. Korean Math. Soc. 2018; 55(5): 1491-1501
Online first article June 18, 2018 Printed September 30, 2018
https://doi.org/10.4134/BKMS.b170854
Copyright © The Korean Mathematical Society.
Paulius Drungilas, Jonas Jankauskas, Grintas Junevicius, Lukas Klebonas, Jonas Siurys
Vilnius University, Mathematik und Statistik, Montanuniversit\"at Leoben, Vilnius University, Vilnius University, Vilnius University
Polynomials with all the coefficients in $\{ 0,1\}$ and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in $\{ -1,1\}$ are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial $X^a+X^b+X^c+1$, $15>a>b>c>0$, has a Littlewood multiple of smallest possible degree which can be as large as $32765$.
Keywords: Borwein polynomial, Littlewood polynomial, Newman polynomial, Salem number, complex Salem number, polynomials of small height
MSC numbers: 11R09, 11Y16, 12D05, 11R06
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