Lehmer's conjecture

Proposed lower bound on the Mahler measure for polynomials with integer coefficients

Lehmer's conjecture, also known as the Lehmer's Mahler measure problem, is a problem in number theory raised by Derrick Henry Lehmer. The conjecture asserts that there is an absolute constant such that every polynomial with integer coefficients satisfies one of the following properties:The Mahler measure of is greater than or equal to . is an integral multiple of a product of cyclotomic polynomials or the monomial , in which case .

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