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On three questions concerning 0 , 1 -polynomials

Michael Filaseta, Carrie Finch, Charles Nicol (2006)

Journal de Théorie des Nombres de Bordeaux

We answer three reducibility (or irreducibility) questions for 0 , 1 -polynomials, those polynomials which have every coefficient either 0 or 1 . The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible 0 , 1 -polynomial. The third is the analogous question for exponents of irreducible 0 , 1 -polynomials.

On three-rowed chomp.

Brouwer, Andries E., Horváth, Gábor, Molnár-Sáska, Ildikó, Szabó, Csaba (2005)

Integers

On traces of the Brandt-Eichler matrices

Juliusz Brzezinski (1998)

Journal de théorie des nombres de Bordeaux

We compute the numbers of locally principal ideals with given norm in a class of definite quaternion orders and the traces of the Brandt-Eichler matrices corresponding to these orders. As an application, we compute the numbers of representations of algebraic integers by the norm forms of definite quaternion orders with class number one as well as we obtain class number relations for some CM-fields.

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