Category:Liouville's Theorem (Number Theory)

This category contains pages concerning Liouville's Theorem (Number Theory):

Let $x$ be an irrational number that is algebraic of degree $n$.

Then there exists a constant $c > 0$ (which can depend on $x$) such that:

$\size {x - \dfrac p q} \ge \dfrac c {q^n}$

for every pair $p, q \in \Z$ with $q \ne 0$.

Source of Name

This entry was named for Joseph Liouville.