Thread: Irrational proof

Assume that √a exists and let α=√a. Prove that there exists a number c>0 such that for all integers q,p and q≠0 we have

|qα-p|>c/q

Originally Posted by ashamrock415

Assume that √a exists and let α=√a. Prove that there exists a number c>0 such that for all integers q,p and q≠0 we have

|qα-p|>c/q

This is a special case of a result of Liouville. There is a proof here (scroll down to the Lemma towards the bottom of the page).