Given any real number and any positive integer , there exist integers and with such that

A slightly weaker form of the theorem states that for every real , there exist integers and with and such that

Given any real number and any positive integer , there exist integers and with such that

A slightly weaker form of the theorem states that for every real , there exist integers and with and such that

Weisstein, Eric W. "Dirichlet's Approximation Theorem." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletsApproximationTheorem.html