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Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves

Joseph H. Silverman — 2012

Journal de Théorie des Nombres de Bordeaux

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  ( / m ) [ X ] by a polynomial of the form 1 + X + + X n for some n ϵ deg ( f ) . We also formulate and prove an analogous statement for elliptic curves.

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