Mathematics – Number Theory
Scientific paper
2010-08-21
Mathematics
Number Theory
22 pages
Scientific paper
A number of authors have proven explicit versions of Lehmer's conjecture for
polynomials whose coefficients are all congruent to 1 modulo m. We prove a
similar result for polynomials f(X) that are divisible in (Z/mZ)[X] by a
polynomial of the form 1+X+...+X^n for some n > \epsilon*deg(f). We also
formulate and prove an analogous statement for elliptic curves.
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