Number theory
M(f) denote the Mahler measure of f.
There exists a constant μ>1 such that for any f(x)∈ℤ[x], M(f)>1 → M(f)≥μ.
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Formal statement
Proof target
import FormalConjectures.Wikipedia.LehmerMahlerMeasureProblem
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "LehmerMahlerMeasureProblem.lehmer_mahler_measure_problem" := by
sorry
end Bounty
Original conjecture (Lean type)
∃ μ,
∀ (f : Polynomial ℤ),
μ > 1 ∧ (LehmerMahlerMeasureProblem.mahlerMeasureZ f > 1 → LehmerMahlerMeasureProblem.mahlerMeasureZ f ≥ μ)Original conjecture source: FormalConjectures/Wikipedia/LehmerMahlerMeasureProblem.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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