abstract
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Powers and polynomials in Z_{m}

Lorenz Halbeisen and Norbert Hungerbühler

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In this article we consider powers and polynomials in the ring
Z_{m}, where *m* in N is arbitrary, and ask for
''reduction formulas''.
Further we consider generalizations of Fermat's little theorem and
Euler's Theorem which allow to replace (in Z_{m}) certain powers
*a*^{b} by a polynomial *f(a)* of degree deg(*f*) which is
strictly less than *b*. Finally, we address the question of the minimal degree
e(*m*) such that every polynomial in Z_{m} can be written as a
polynomial of degree *q* < e(*m*). We give a complete answer to
this question by determining minimal (normed) null-polynomials
modulo *m*.