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

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- September 20th 2010, 07:54 PMashamrock415Irrational 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 - September 21st 2010, 05:44 AMOpalg
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).