Lehmer's conjecture

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 ${\displaystyle \mu >1}$ such that every polynomial with integer coefficients ${\displaystyle P(x)\in \mathbb {Z} [x]}$ satisfies one of the following properties:

There are a number of definitions of the Mahler measure, one of which is to factor ${\displaystyle P(x)}$ over ${\displaystyle \mathbb {C} }$ as

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