Lehmer's conjecture, also known as the Lehmer's Mahler measure problem, is a problem in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...
raised by
Derrick Henry Lehmer.
The conjecture asserts that there is an absolute constant
such that every
polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...
with integer coefficients