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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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).
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