Hurwitz's theorem (number theory)
In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that
The hypothesis that ξ is irrational cannot be omitted. Moreover the constant is the best possible; if we replace by any number and we let then there exist only finitely many relatively prime integers m, n such that the formula above holds.
The theorem is equivalent to the claim that the Markov constant of every number is larger than.
