Abstract
AbstractWe prove that every real algebraic integer α is expressible by a difference of two Mahler measures of integer polynomials. Moreover, these polynomials can be chosen in such a way that they both have the same degree as that of α, say d, one of these two polynomials is irreducible and another has an irreducible factor of degree d, so that α = M(P)−bM(Q) with irreducible polynomials P,Q ∈ ℤ[X] of degree d and a positive integer b. Finally, if d ⩽ 3, then one can take b = 1.
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