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 μ > 1 {\displaystyle \mu >1} such that every polynomial with integer coefficients P ( x ) ∈ Z [ x ] {\displaystyle P(x)\in \mathbb {Z} [x]} satisfies one of the following properties: The Mahler measure M ( P ( x ) ) {\displaystyle {\mathcal {M}}(P(x))} of P ( x ) {\displaystyle P(x)} is greater than or equal to μ {\displaystyle \mu } .