Abstract
These numbers have been studied recently by D. H. Lehmer in another connection.2 2. Let W denote the residue class of all polynomials of degree N which are congruent to A(x) modulo p, and consider for each polynomial A'(x) of a the highest power of p which divides A(n) (A') = Res { xpn x, A'(x) }. For a given value of n, this power is either zero for every such polynomial, or else a positive integer, which may be thought of as arbitrarily large if the resultant happens to vanish. If the power is not zero there clearly exist polynomials of 21 for which it assumes a minimum value. We denote this minimum by pqm, so that we shall have for some polynomial A'(x) of degree N,
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